Physicists Frame Life as Vehicle Driving Cosmic Entropy Increase
Veritasium
Earth sustains biological order not by hoarding solar energy, but by converting each concentrated solar photon into 20 diffuse infrared photons to dissipate universal energy.
AI-assisted summary of The Most Misunderstood Concept in Physics — original source. Check the original for full context.
Source published:
Key ideas
- Earth maintains thermodynamic equilibrium by radiating into space the exact same quantity of energy it absorbs from the sun, but it trades a single high-energy solar photon for roughly 20 dispersed, lower-energy infrared photons. (14:50)
- Sadi Carnot demonstrated that heat engine efficiency is fundamentally capped by the ratio of absolute temperatures between hot and cold reservoirs, not engine design or material choice. (6:22)
- Entropy is not merely disorder but a statistical measure of energy dispersal; backward heat flow is not physically forbidden, but exponentially improbable as particle count scales. (11:24)
- Black holes represent the primary entropy sinks of the modern cosmos, with Sagittarius A* holding roughly 10^91 Boltzmann constants—thousands of times more entropy than the entire post-Big Bang observable universe. (21:36)
- Complex structures like galaxies, weather systems, and biological life emerge exclusively during the intermediate transition between low and high entropy rather than at either extreme. (25:00)
Detailed notes
## Background Published on YouTube by the educational channel Veritasium (hosted by Derek Muller) on July 1, 2023, this video explores entropy, described in the show notes as one of the most important yet least understood concepts in all of physics. The description highlights the collaborative physics research behind the presentation alongside references to foundational historical and modern papers.
## TL;DR The video deconstructs common misconceptions about entropy, explaining that it represents the natural statistical tendency of concentrated energy to disperse rather than mere macroscopic disorder. Tracing the concept from Sadi Carnot's 19th-century analysis of heat engine efficiency through Rudolf Clausius and Ludwig Boltzmann's statistical mechanics, Derek Muller shows how the Second Law of Thermodynamics governs everyday phenomena. Crucially, the Earth does not retain net energy from the Sun but rather absorbs low-entropy, high-energy photons and reradiates them as diffuse infrared photons. This cosmic gradient drives biological complexity, explains why time flows in only one direction, and charts the eventual thermodynamic path toward the heat death of the universe.
## Atmosphere & style The presentation blends street-level curiosity with cinematic, mind-expanding scientific storytelling. Derek Muller acts as an approachable, inquisitive guide whose casual man-on-the-street interviews smoothly transition into rigorous historical narratives and elegant theoretical physics. The tone evolves from playful confusion to an awe-inspiring, almost poetic appreciation of existence, framing human life and cosmic structure as brief, magnificent eddies flourishing in the intermediate zone between absolute order and ultimate thermodynamic dissolution.
## Bulletin - [14:50](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=890s) Earth maintains thermodynamic equilibrium by radiating into space the exact same quantity of energy it absorbs from the sun, but it trades a single high-energy solar photon for roughly 20 dispersed, lower-energy infrared photons. - [06:22](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=382s) Sadi Carnot demonstrated that heat engine efficiency is fundamentally capped by the ratio of absolute temperatures between hot and cold reservoirs, not engine design or material choice. - [11:24](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=684s) Entropy is not merely disorder but a statistical measure of energy dispersal; backward heat flow is not physically forbidden, but exponentially improbable as particle count scales. - [21:36](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=1296s) Black holes represent the primary entropy sinks of the modern cosmos, with Sagittarius A* holding roughly 10^91 Boltzmann constants—thousands of times more entropy than the entire post-Big Bang observable universe. - [25:00](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=1500s) Complex structures like galaxies, weather systems, and biological life emerge exclusively during the intermediate transition between low and high entropy rather than at either extreme.
## Key takeaways - [00:00](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=0s) Energy conservation dictates that over long timescales, the Earth must radiate into space the exact amount of energy it receives from the sun to prevent runaway warming. - [04:12](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=252s) Sadi Carnot formulated an idealized reversible engine operating between two thermal reservoirs to determine the absolute theoretical limit of thermodynamic efficiency. - [06:22](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=382s) Carnot efficiency depends solely on reservoir temperatures (eta = 1 - T_cold / T_hot), meaning 100% efficiency requires an impossible cold reservoir at absolute zero. - [09:05](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=545s) Rudolf Clausius formulated entropy to quantify irreversible energy dispersal, establishing that universal entropy relentlessly tends toward a maximum. - [11:24](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=684s) Ludwig Boltzmann showed that heat flows spontaneously from hot to cold due to statistical counting: thermal equilibrium corresponds to overwhelmingly numerous microstates compared to non-equilibrium configurations. - [14:50](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=890s) Local entropy decreases, such as domestic air conditioning or cellular organization, must always be compensated by a greater net entropy increase in the wider environment. - [14:50](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=890s) Life functions as an open thermodynamic engine, driving metabolic processes by transforming concentrated solar radiation into diffuse planetary infrared waste. - [18:10](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=1090s) Dissipative adaptation suggests that matter driven by external energy naturally self-organizes into structures that accelerate entropy production. - [19:11](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=1151s) Under the Past Hypothesis, the early universe occupied an exceptionally low-entropy state because matter was smoothly distributed rather than clumped by gravity. - [21:36](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=1296s) Jacob Bekenstein and Stephen Hawking revealed that black hole entropy is proportional to event horizon surface area, with black holes dominating cosmic entropy today. - [23:31](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=1411s) The thermodynamic arrow of time is defined by the irreversible progression from statistically improbable low-entropy states toward high-probability equilibrium. - [23:31](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=1411s) The heat death of the universe represents an ultimate statistical equilibrium where no work can be extracted and the macroscopic arrow of time disappears. - [25:00](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=1500s) Structural and biological complexity peaks during the dynamic intermediate phase between low and high entropy, while both pure order and maximum entropy lack complexity.
## Detailed walkthrough ### [00:00](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=0s) The Street Interview: What Does Earth Get from the Sun?
A fundamental concept in physics governs everything from microscopic molecular collisions to colossal atmospheric storms, shaping the evolution of the universe from the Big Bang to its eventual demise. It may determine why time flows only forward and even explain why life itself emerged. Yet, despite its sweeping importance, it remains deeply misunderstood. To highlight the widespread confusion, Derek Muller takes to the street to pose a deceptively basic question to passersby: what does the Earth get from the sun?
People readily reply with heat, light, warmth, ultraviolet rays that produce vitamin D, and, broadly, energy. Derek agrees, but then follows up with a crucial second question: relative to the amount of energy the Earth absorbs from the sun, how much does it radiate back out into space? The responses immediately reveal intuitive misconceptions. People guess that Earth retains most of it, offering estimates like 20% or 70% radiated back. One person reasons, “Probably not as much, I, you know, I don't believe it's just radiating right back,” while another explains, “Because we use some of the energy.” But energy cannot simply be used up or disappear.
As Derek explains, if the Earth absorbed more energy than it released, it would continuously heat up, creating an unlivable catastrophe. As Derek puts it: “For most of the earth's history, it should be exactly the same amount of energy in from the sun as earth radiates into space.” This leaves the interviewees visibly puzzled. If the total energy entering the Earth is equal to the energy radiated back out into space, what is Earth actually receiving? While one bystander jokes, “It gives us a nice tan,” the true answer requires examining an intellectual breakthrough that began two centuries ago.
- Passersby intuitively assume Earth absorbs and holds onto most solar energy to power civilization and natural processes. - Because energy is conserved, the net incoming solar radiation must balance the outgoing terrestrial thermal radiation over the long term to maintain a steady planetary temperature.
---
[02:15](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=135s) Sadi Carnot and the Search for Engine Efficiency
In the winter of 1813, France faced invasion from the allied armies of Austria, Prussia, and Russia. Sadi Carnot, a 17-year-old student and the son of one of Napoleon Bonaparte’s generals, wrote directly to Napoleon on December 29 requesting permission to fight on the front lines. Preoccupied with the war, the Emperor never replied. A few months later, when enemy forces marched on Paris, Carnot and his fellow students took up arms to defend a chateau east of the capital. They were hopelessly outmatched, Paris fell within a single day, and the young Carnot was left devastated by the defeat.
Seven years later, Carnot traveled to Prussia to visit his exiled father, who was not only a military leader but also an accomplished physicist with published work on mechanical energy transfer. Their conversations gravitated toward the defining technology of the industrial age: the steam engine. Steam engines were rapidly reshaping global infrastructure by propelling ships, draining mine shafts, and dredging harbors. Carnot realized that the economic and military supremacy of nations would belong to whoever possessed the most powerful, fuel-efficient engines.
At the time, French engineering lagged noticeably behind British industry. The most advanced steam engines in existence managed to convert only about 3% of their thermal energy into usable mechanical work. Determined to restore France’s national standing, Carnot spent the next three years investigating the fundamental physics of heat engines to determine whether there was an absolute upper limit to their efficiency.
- On December 29, 1813, 17-year-old Carnot wrote to Napoleon asking to serve, but Paris fell shortly after in a one-day battle. - Contemporary early-19th-century steam engines operated at an abysmal conversion efficiency of approximately 3%.
---
[04:12](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=252s) The Ideal Carnot Engine and Reversibility
To analyze heat engines without the messiness of real-world flaws, Carnot conceived a theoretical, frictionless engine that suffered no heat losses to the ambient surroundings. This idealized machine operates between two large thermal reservoirs: a hot metal bar and a cold metal bar. The working mechanism consists of an insulated cylinder filled with air, sealed by a movable piston connected to a heavy flywheel, with a conductive base allowing heat transfer exclusively through the bottom.
```mermaid flowchart TD accTitle: The Four Stages of the Carnot Cycle accDescr: Step by step progression of the Carnot cycle through isothermal and adiabatic expansion followed by isothermal and adiabatic compression. subgraph HotStage ["Hot Reservoir Phase"] A["1. Isothermal Expansion<br>(Chamber on hot bar; gas absorbs heat and expands, pushing piston)"] B["2. Adiabatic Expansion<br>(Hot bar removed; gas continues expanding and cools to cold bar temperature)"] end subgraph ColdStage ["Cold Reservoir Phase"] C["3. Isothermal Compression<br>(Chamber on cold bar; flywheel pushes piston, dumping heat into cold bar)"] D["4. Adiabatic Compression<br>(Cold bar removed; gas compressed further, heating to initial hot state)"] end A --> B B --> C C --> D D --> A ```
The cycle begins with the air inside the cylinder slightly below the hot bar's temperature. Bringing the hot bar against the base causes the gas to expand at constant temperature as heat enters, driving the piston upward and turning the flywheel. The hot bar is then pulled away, allowing the air to continue expanding adiabatically; because no new heat enters, the gas cools until it matches the temperature of the cold bar. Next, the cold bar is brought into contact with the base while the momentum of the flywheel forces the piston back down, compressing the gas and discharging heat into the cold sink. Finally, the cold bar is detached, and the flywheel compresses the gas further, warming it back up to just below the hot bar's temperature so the cycle can repeat.
Carnot recognized that this idealized engine is entirely reversible. If the flywheel's momentum is driven in the opposite direction, the gas expands to draw heat out of the cold bar, gets compressed, and deposits that exact amount of heat back into the hot bar. As Derek notes: “However many cycles were run in the forward direction, you could run the same number in reverse, and at the end, everything would return to its original state with no additional input of energy required.” Because an ideal engine can run forward and backward indefinitely without altering the total state of the system or its surroundings, running it produces no permanent change in the universe.
---
[06:22](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=382s) Efficiency Limits and the Kelvin Scale
A fully reversible engine might seem capable of 100% efficiency, but Carnot proved this is mathematically impossible. The net mechanical energy added to the flywheel during each cycle equals the heat absorbed from the hot reservoir minus the heat rejected into the cold reservoir. The efficiency is simply this net work divided by the heat input from the hot side. Because the gas is hotter and under higher pressure during the expansion stroke than during the cold compression stroke, the work done by the expanding gas exceeds the work required to compress it back down. Still, some heat must always be dumped into the cold reservoir to reset the piston.
Decades later, Lord Kelvin realized that Carnot's ideal engine established an absolute temperature scale independent of any specific material. If a gas could expand until it cooled to a state where molecular motion ceased entirely, the particles would exert zero pressure on the piston. Compressing the gas on the cold side would then require zero mechanical work, meaning no waste heat would be rejected, yielding an engine of 100% efficiency. This theoretical zero-point defines absolute zero on the Kelvin scale.
Because the heat absorbed and rejected in an ideal cycle is directly proportional to absolute temperature, the efficiency of a Carnot engine simplifies to $\eta = 1 - (T_{\text{cold}} / T_{\text{hot}})$. As Derek emphasizes: “What we have learned is that the efficiency of an ideal heat engine doesn't depend on the materials or the design of the engine, but fundamentally on the temperatures of the hot and cold sides.” Achieving 100% thermal efficiency would require either an infinitely hot heat source or a cold sink at absolute zero—both physically unreachable. In Carnot's era, high-pressure steam engines operated at temperatures around 160 °C, establishing a theoretical Carnot efficiency ceiling of 32%, far above their real-world 3% performance.
- Maximum thermal efficiency is strictly determined by the ratio of the absolute temperatures of the heat reservoirs: $\eta = 1 - \frac{T_C}{T_H}$. - 19th-century steam engines operating at 160 °C (around 433 K) and exhausting near ambient temperatures had a maximum theoretical limit of 32%.
---
[09:05](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=545s) Rudolf Clausius, Entropy, and the Second Law
Real heat engines fall far short of theoretical limits because they are plagued by internal friction, imperfect heat transfer across fluctuating temperatures, and uncontained thermal dissipation into the surrounding air, cylinder walls, and flywheel axles. Once heat leaks into the wider environment, it disperses randomly into microscopic vibrations that cannot be gathered back together. The mechanical cycle becomes strictly irreversible. Even though the first law of thermodynamics guarantees that total energy is conserved, the energy undergoes a qualitative decline. As Derek observes: “Energy is most usable when it is concentrated and less usable when it's spread out.”
In the 1850s and 1860s, German physicist Rudolf Clausius analyzed Carnot's thermodynamic framework and created a mathematical formulation to track this dissipation of energy, naming the property *entropy*. When energy is tightly concentrated within a hot source, entropy is low and the capacity to do useful work is high. When that energy disperses into the cooler environment, cylinder casing, and mechanical bearings, entropy increases, rendering that energy unavailable for work.
In 1865, Clausius distilled thermodynamics down to two fundamental tenets: “First, the energy of the universe is constant. And second, the entropy of the universe tends to a maximum.” This second law dictates why heat flows spontaneously from hot objects to cold ones, why an unconstrained gas expands to fill its container, and why perpetual motion machines are an impossibility. Derek points out that while popular science typically equates entropy with "disorder"—reflecting how systems naturally evolve toward mixed and random states—the most accurate physical intuition is simply “the tendency of energy to spread out.”
- Real-world engines are irreversible because friction and heat dissipation disperse concentrated energy into the surrounding environment. - Clausius coined the term *entropy* to quantify how dispersed energy becomes relative to absolute temperature. - The two fundamental laws of thermodynamics formulated by Clausius (1865): 1. The total energy of the universe remains constant. 2. The total entropy of the universe tends toward a maximum.
[11:24](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=684s) Boltzmann’s Statistical Insight and the Improbability of Heat Reversal
The fundamental laws of physics operate identically whether running forwards or backwards in time, raising the question of where the observed arrow of time actually originates. To demonstrate this on a microscopic scale, Derek Muller introduces a simplified model of two small metal bars brought together, one hot and one cold, containing just eight atoms each. The thermal energy of each atom corresponds to the number of discrete energy packets it holds; the more packets it contains, the more vigorously it vibrates. Starting with seven packets in the left bar and three in the right, these packets continuously hop at random between atoms across the lattice while the total energy remains constant. When the two bars touch, packets hop across the boundary, creating countless possible energy arrangements where every single microscopic configuration is equally likely.
```mermaid flowchart LR accTitle: Energy Packet Redistribution Between Two Contacting Solids accDescr: Microscopic hopping of energy packets leads to macroscopic thermal equilibrium based on high-probability microstates.
subgraph Initial["Initial Non-Equilibrium State"] Hot["Hot Bar: 7 Packets"] Cold["Cold Bar: 3 Packets"] Hot <-->|"Energy Exchange"| Cold end
subgraph States["Statistical Microstates"] Improbable["Cold to Hot: 9 on Left / 1 on Right<br/>(91,520 configurations)"] Probable["Equilibrium: 5 on Left / 5 on Right<br/>(627,264 configurations)"] end
Initial --> States ```
If one takes a snapshot after contact, it is entirely possible to find nine packets in the left bar and only one in the right. This represents heat flowing from cold to hot—an apparent decrease in entropy. Ludwig Boltzmann resolved this apparent contradiction by recognizing that heat flowing backwards is not fundamentally forbidden, but merely statistically improbable: “Heat flowing from cold to hot is not impossible, it’s just improbable.” While there are 91,520 configurations where nine packets sit in the left bar, there are 627,264 configurations where energy divides evenly with five packets in each bar, making thermal equilibrium almost seven times more probable.
Even in this eight-atom system, there is still an overall 10.5% chance that the hot bar ends up with more energy than it started with. However, scaling the model up to 80 atoms per bar with 100 energy packets (starting 70 on the left and 30 on the right) drops the probability of the left solid getting hotter to just 0.05%. In everyday macroscopic objects containing roughly 100 trillion trillion ($10^{26}$) atoms and vastly more energy packets, the chance of spontaneous heat concentration approaches zero so closely that it never occurs. Muller illustrates this using a Rubik's cube: starting from a solved state and applying blind, random turns inevitably scrambles it. Because there is only one solved configuration, a handful of nearly solved states, and quintillions of disordered arrangements, random actions overwhelmingly drive systems from rare, ordered configurations into overwhelmingly abundant messy ones.
- Eight atoms per bar with a 7:3 packet split: 91,520 microstates for a 9:1 split vs. 627,264 microstates for a 5:5 split. - Chance of left bar ending hotter in the 8-atom toy model: 10.5%. - Chance of left solid ending hotter in an 80-atom system (70:30 starting split): 0.05%. - Real-world macroscopic solids contain on the order of 100 trillion trillion atoms.
---
[14:50](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=890s) Local Order Paid by Global Entropy: Air Conditioners and the Sun
If the natural law of the universe is for energy to disperse and disorder to grow, localized processes that concentrate energy seem puzzling. An air conditioner cools an already cool room by dumping heat into an already hotter outdoors, clearly decreasing the entropy inside the house. However, this local decrease is only achieved by generating a far larger quantity of entropy elsewhere in the broader system. Running the air conditioner requires electricity from a power plant where concentrated chemical energy stored in coal is liberated, creating vast amounts of thermal waste at the generation site, dispersing heat through miles of transmission lines, and venting friction and electrical losses from fans and compressors. The localized drop in domestic entropy is heavily outmatched by the total entropy generated to power the device: “Whatever decrease in entropy is achieved at the house is more than paid for by an increase in entropy required to make that happen.”
This mechanism explains how complex order and life persist on Earth without violating thermodynamics. If Earth were an isolated, closed system, all internal temperature differences would flatten out, chemical complexity would rot and homogenize, and all life would perish. Earth avoids this equilibrium because it is an open system bathed in continuous radiation from the sun. The sun delivers a continuous inflow of low-entropy, concentrated energy. Terrestrial life captures this bundled energy—plants synthesize sugars via photosynthesis, herbivores consume plants, and carnivores consume herbivores. At each link in the food chain, energy cascades outward and disperses further.
Muller discusses the planetary balance sheet with an off-camera colleague, jokingly reminding him: “I'm a PhD physicist,” to which the colleague replies, “I trust you.” In steady state, Earth emits the exact same total quantity of energy back into space as it absorbs from solar radiation. The entropy generation of this planetary exchange is revealed by photon counting: for every single high-energy, low-entropy solar photon Earth absorbs, it radiates roughly 20 lower-energy infrared photons back into the cosmic void. Every terrestrial phenomenon—winds, oceanic currents, biological metabolism, sleeping, and ecosystems—is powered entirely along this gradient of converting few energetic photons into 20 times as many diffuse ones.
```mermaid flowchart TD accTitle: Earth Thermodynamic Budget and Photon Multiplication accDescr: Earth absorbs concentrated solar photons and re-emits dispersed infrared photons, driving biological and physical processes.
Sun["Sun: Emits 1 High-Energy Photon<br/>(Concentrated Low Entropy)"] -->|"Absorbed"| Earth["Earth System<br/>(Photosynthesis, Weather, Metabolism)"] Earth -->|"Dissipated as Waste Heat"| Space["Space: Emits 20 Low-Energy Photons<br/>(Dispersed High Entropy)"] ```
---
[18:10](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=1090s) Dissipative Structures, Jeremy England, and the Origin of Life
Because life dramatically accelerates the dispersion of energy, several physicists suggest that life is not an improbable accident opposing thermodynamics, but rather a direct vehicle of the Second Law. If the cosmos drives toward maximizing entropy, self-organizing structures emerge because they convert low entropy into high entropy far more efficiently than inanimate matter. In marine environments, for instance, surface waters enriched with cyanobacteria and organic material generate between 30% and 680% more entropy than identical barren seawater.
Physicist Jeremy England expanded this concept into the physics of self-replication and driven assembly. When an arbitrary collection of matter is subjected to an external driving stream of concentrated energy, physical forces naturally select and stabilize configurations capable of absorbing and dissipating that energy into the environment. Over time, matter undergoes dissipative adaptation, evolving increasingly sophisticated dissipators until complex lifelike structures emerge. Muller quotes Jeremy England's formulation directly: “You start with a random clump of atoms, and if you shine light on it for long enough, it should not be so surprising that you get a plant.”
- Surface seawater containing cyanobacteria and organic matter increases entropy production by 30% to 680% compared to abiotic seawater. - Jeremy England’s dissipative adaptation framework models living systems as optimized structures that unpack and discard concentrated free energy into surrounding heat baths.
---
[19:11](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=1151s) Gravity, the Big Bang, and the Cosmic Past Hypothesis
Tracking the chain of low entropy backwards reveals a cosmic puzzle. If Earth relies on the sun's low entropy, the sun owes its concentrated energy to the universe at large. Because cosmic entropy increases monotonically over time, entropy must have been lower yesterday, lower still millions of years ago, and minimal at the moment of the Big Bang. This requirement is known in cosmology as the *past hypothesis*. While it does not explain why the initial conditions were so ordered, it states that an exceptionally low-entropy starting condition was essential for galaxies, stars, and life to form.
This poses a major paradox: the infant universe was hot, dense, and nearly uniform, with temperature variations across space not exceeding 0.001% (one part in 100,000). In a standard gas, complete uniformity denotes maximum entropy. The missing variable in that assessment is gravity. In a self-gravitating system, a smooth, uniform distribution of mass is extraordinarily unnatural and improbable; gravity's natural drive is to pull matter into dense clumps. Thus, an ultra-smooth early universe represents an extremely low-entropy state:
```mermaid flowchart LR accTitle: Gravitational Entropy Production Across Cosmic Time accDescr: The early smooth matter distribution collapses under gravity, releasing potential energy and driving star formation and entropy growth.
Uniform["Uniform Gas Post-Big Bang<br/>(Low Gravitational Entropy)"] -->|"Gravitational Collapse"| Clumping["Clumping into Stars & Galaxies<br/>(Potential Energy to Kinetic Energy)"] Clumping -->|"Collisions & Radiation"| Dissipation["Thermal Dissipation & Black Holes<br/>(Massive Entropy Increase)"] ```
As the cosmos expanded and cooled, gravitational instability drew matter into denser pockets. This collapse converted enormous reserves of gravitational potential energy into kinetic energy. When particles collided during collapse, kinetic energy degraded into heat, dissipating useful energy and increasing overall entropy while forging stars, planets, and galaxies.
At the beginning of the universe, total entropy stood at roughly $10^{88}$ Boltzmann constants ($k_\text{B}$). In the present epoch, the observable stellar mass accounts for about $9.5 \times 10^{80}\ k_\text{B}$. The combined interstellar and intergalactic medium contains nearly ten times that amount, though still a tiny fraction of the initial universal value. Considerably larger pools of ordinary entropy reside in cosmic relic neutrinos and the photons of the Cosmic Microwave Background (CMB).
---
[21:36](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=1296s) Black Hole Thermodynamics: Bekenstein and Hawking
In 1972, Jacob Bekenstein proposed that black holes possess entropy and that this entropy is directly proportional to the surface area of their event horizons, meaning a black hole's entropy increases whenever it swallows matter and expands. Mainstream physicists initially dismissed the proposal as absurd. Classical thermodynamics dictates that anything endowed with entropy must also possess a non-zero temperature, and any body with a finite temperature must emit blackbody radiation—meaning a black hole could not be entirely black.
Stephen Hawking set out to disprove Bekenstein's conjecture using quantum field theory in curved spacetime. Instead of debunking it, Hawking discovered that quantum effects near the event horizon cause black holes to emit a steady stream of thermal radiation, now celebrated as Hawking radiation:
```mermaid flowchart TD accTitle: Development of Black Hole Thermodynamics accDescr: Bekenstein's controversial area-entropy conjecture confirmed by Hawking's calculation of black hole temperature and radiation.
Bekenstein["1972: Jacob Bekenstein proposes<br/>Entropy ∝ Horizon Surface Area"] Skepticism["Physics Community Objects:<br/>Finite Entropy implies Temperature & Radiation"] Hawking["Stephen Hawking attempts disproof<br/>Discovers Hawking Radiation & validates Bekenstein"]
Bekenstein --> Skepticism Skepticism --> Hawking ```
Hawking's calculations confirmed that black holes have both a definite temperature and enormous entropy, refining Bekenstein's model into the Bekenstein-Hawking entropy formula. For stellar and supermassive black holes, this temperature is minuscule. The supermassive black hole at the core of the Milky Way (Sagittarius A*) has a temperature of approximately one hundred trillionth of a Kelvin ($10^{-14}\text{ K}$), radiating far too weakly to be detected against the cosmic background.
Hawking's equations revealed that black holes are the dominant repositories of entropy in the cosmos: - Sagittarius A* contains roughly $10^{91}$ Boltzmann constants of entropy—1,000 times more entropy than the entire observable universe possessed shortly after the Big Bang, and ten times more than all other cosmic particles combined. - All black holes across the observable universe hold a combined entropy of approximately $3 \times 10^{104}\ k_\text{B}$. - Because black holes concentrate virtually all cosmic entropy, the early post-Big Bang universe held a mere $0.000000000000003\%$ ($3 \times 10^{-15}\%$) of the entropy present in the universe today.
[23:31](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=1411s) The Arrow of Time and the Heat Death of the Universe
Every dynamic event in cosmic history—from the formation of planetary systems and the collision of galaxies to crashing asteroids, dying stars, and the emergence of life itself—is driven by a single fundamental reality: the universe began in a state of remarkably low entropy, and that entropy has been climbing ever since. Crucially, physical transformations happen in only one direction. We observe asteroids shattering upon impact, but we never witness an asteroid spontaneously "uncrash," just as we never see a mature solar system unmix itself back into a pristine, dispersed cloud of primordial gas and dust. This fundamental asymmetry is what separates the past from the future. As Derek Muller explains, “The fact that we are going from unlikely to more likely states is why there is an arrow of time.”
```mermaid flowchart TD accTitle: The Thermodynamic Arrow of Time accDescr: Progression from the Big Bang's low-entropy state through cosmic evolution to the ultimate heat death of the universe.
subgraph Past ["Low Entropy (Past)"] A["Big Bang: highly improbable, low-entropy state"] end
subgraph Present ["Increasing Entropy (Present)"] B["Cosmic Evolution: stars, galaxies, and life flourish"] end
subgraph Future ["Maximum Entropy (Distant Future)"] C["Evaporation of last black holes (>10¹⁰⁰ years)"] D["Heat Death: energy uniformly spread, arrow of time vanishes"] end
A --> B B --> C C --> D ```
This thermodynamic trajectory is projected to continue until energy is distributed so completely and evenly that no thermodynamic work can ever be extracted again. This ultimate state of stagnation is known as the heat death of the universe. In the inconceivably distant future—more than $10^{100}$ years from now, once the final black holes have completely evaporated through Hawking radiation—the universe will reach its most probable statistical state. At that point, even across vast cosmic distances, moving forward in time will be physically indistinguishable from moving backward, and the macroscopic arrow of time will cease to exist.
- Everything dynamic in the universe relies on the gradient created by its initial low-entropy state. - Irreversible macroscopic processes establish the directionality of time. - The heat death represents the ultimate equilibrium state of maximum probability and maximum entropy. - After black holes evaporate past $10^{100}$ years, macroscopic temporal directionality disappears entirely.
---
[25:00](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=1500s) The Emergence of Complexity Between Extremes
While it may seem that entropy is simply a destructive force dragging reality toward the dullest conceivable fate, high entropy should not be mistaken as the sole enemy of form and beauty. Just as maximum entropy corresponds to minimal complexity, a state of absolute minimum entropy is equally devoid of complex behavior. Derek illustrates this using the everyday example of tea and milk. Held completely separate in a mug and pitcher, the liquids have low entropy but are static and uninteresting. However, the instant the milk is poured into the hot tea, intricate, swirling plumes and delicate fractal patterns bloom across the liquid before eventually fading away into a bland, uniform mixture.
```mermaid flowchart LR accTitle: Complexity Curve Relative to Entropy accDescr: Charting complexity across low, intermediate, and maximum entropy states using the milk and tea analogy.
A["Separate Tea & Milk<br>(Low Entropy / Low Complexity)"] --> B["Active Mixing & Eddies<br>(Medium Entropy / Peak Complexity)"] B --> C["Uniform Mixture<br>(Maximum Entropy / Low Complexity)"] ```
Both extremes—pure order and pure disorder—are fundamentally poor in structure. Complex, organized phenomena do not exist at the absolute extremes; they emerge and thrive exclusively in the intermediate transition zone while entropy is on the rise. Derek highlights our place within this ongoing thermodynamic cascade: “Both low and high entropy are low in complexity. It's in the middle where complex structures appear and thrive.” Because human existence and the biosphere are situated right in this sweet spot, he urges viewers to take advantage of the universe's remaining low entropy while it lasts.
- Maximum entropy features low complexity because everything is uniformly mixed and homogeneous. - Pure low entropy also features low complexity due to its static, unmixed separation. - Rich, intricate structures (including living organisms) emerge exclusively during the intermediate transition from low to high entropy.
---
[25:47](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=1547s) Equipping Your Mind: Brilliant.org
Reflecting on the overarching lessons of thermodynamics, Derek notes that having the proper conceptual frameworks empowers people to demystify complex systems, remarking: “With the right tools, we can understand just about anything, from a cup of tea cooling down to the evolution of the entire universe.” He transitions to highlighting the video's sponsor, Brilliant.org, as a practical platform for building those analytical capabilities across STEM fields, including mathematics, physics, data science, and programming.
Rather than relying on passive lectures, Brilliant emphasizes active, problem-based learning. Derek highlights their interactive course, "Thinking in Code," which uses a drag-and-drop environment to teach foundational programming principles such as nesting and conditional logic without getting bogged down in syntax errors. The course guides learners through tangible challenges—ranging from programming a virtual robot to designing real-world automation scripts, such as setting phone reminders or filtering prospective matches on a dating app. He concludes by offering a 30-day free trial along with a 20% discount on an annual premium subscription for the first 200 subscribers who visit the dedicated link.
- Brilliant provides guided interactive pathways across physics, programming, math, and data science. - The "Thinking in Code" curriculum introduces essential programming constructs, including conditionals and nested logic, via intuitive drag-and-drop interfaces. - The learning methodology focuses on practical applications and immediate feedback to develop real intuition. - Viewers are offered a 30-day free trial and a 20% discount on an annual premium tier at `brilliant.org/veritasium`.
## Notable quotes > [11:24](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=684s) Heat flowing from cold to hot is not impossible, it’s just improbable. — Ludwig Boltzmann
> [18:10](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=1090s) You start with a random clump of atoms, and if you shine light on it for long enough, it should not be so surprising that you get a plant. — Jeremy England
> [25:00](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=1500s) Both low and high entropy are low in complexity. It's in the middle where complex structures appear and thrive. — Derek Muller
> [23:31](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=1411s) The fact that we are going from unlikely to more likely states is why there is an arrow of time. — Derek Muller
> [09:05](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=545s) Energy is most usable when it is concentrated and less usable when it's spread out. — Derek Muller
> [06:22](https://www.youtube.com/watch?v=DxL2HoqLbyA&t=382s) What we have learned is that the efficiency of an ideal heat engine doesn't depend on the materials or the design of the engine, but fundamentally on the temperatures of the hot and cold sides. — Derek Muller
## Mentioned Sadi Carnot, Napoleon Bonaparte, Lord Kelvin, Rudolf Clausius, Ludwig Boltzmann, Jeremy England, Jacob Bekenstein, Stephen Hawking, Derek Muller, Brilliant.org, Sagittarius A*, Elements of Truth, Snatoms
## Video description One of the most important, yet least understood, concepts in all of physics. Head to https://brilliant.org/veritasium to start your free 30-day trial, and the first 200 people get 20% off an annual premium subscription.
In 2025, we launched the Elements of Truth game on Kickstarter and were thrilled by the response. We’re now in the final stages of production, with Kickstarter rewards shipping soon. If you missed the campaign, you can now pre-order the retail edition through our new website here - https://ve42.co/EntropyDes
If you're looking for a molecular modeling kit, try Snatoms - a kit I invented where the atoms snap together magnetically: https://snatoms.com
We have a tabletop game launching! Pledge your support now - https://ve42.co/KickStarterD
▀▀▀ A huge thank you to those who helped us understand different aspects of this complicated topic - Dr. Ashmeet Singh, Supriya Krishnamurthy, Dr. Jos Thijssen, Dr. Bijoy Bera, Dr. Timon Idema, Álvaro Bermejillo Seco and Dr. Misha Titov.
▀▀▀ References: Carnot, S. (1824). Reflections on the motive power of heat: and on machines fitted to develop that power. - https://ve42.co/Carnot1890
Harnessing The True Power Of Atoms | Order And Disorder Documentaries, Spark via YouTube - https://ve42.co/OrderDisorder
A better description of entropy, Steve Mould via YouTube - https://ve42.co/Mould2016
Dugdale, J. S. (1996). Entropy and its physical meaning. CRC Press. - https://ve42.co/Dugdale1996
Schroeder, D. V. (1999). An introduction to thermal physics. - https://ve42.co/Schroeder2021
Fowler, M. Heat Engines: the Carnot Cycle, University of Virginia. - https://ve42.co/Fowler2023
Chandler, D.L. (2010). Explained: The Carnot Limit, MIT News - https://ve42.co/Chandler2010
Entropy, Wikipedia - https://ve42.co/EntropyWiki
Clausius, R. (1867). The mechanical theory of heat. Van Voorst. - https://ve42.co/Clausius1867
What is entropy? TED-Ed via YouTube - https://ve42.co/Phillips2017
Thijssen, J. (2018) Lecture Notes Statistical Physics, TU Delft.
Schneider, E. D., & Kay, J. J. (1994). Life as a manifestation of the second law of thermodynamics. Mathematical and computer modelling, 19(6-8), 25-48. - https://ve42.co/Schneider1994
Lineweaver, C. H., & Egan, C. A. (2008). Life, gravity and the second law of thermodynamics. Physics of Life Reviews, 5(4), 225-242. - https://ve42.co/Lineweaver2008
Michaelian, K. (2012). HESS Opinions" Biological catalysis of the hydrological cycle: life's thermodynamic function". Hydrology and Earth System Sciences, 16(8), 2629-2645. - https://ve42.co/Michaelian2012
England, J. L. (2013). Statistical physics of self-replication. The Journal of chemical physics, 139(12), 09B623_1. - https://ve42.co/England2013
England, J. L. (2015). Dissipative adaptation in driven self-assembly. Nature nanotechnology, 10(11), 919-923. - https://ve42.co/England2015
Wolchover, N. (2014). A New Physics Theory of Life, Quantamagazine - https://ve42.co/Wolchover2014
Additional References: https://ve42.co/EntropyRefs
▀▀▀ Special thanks to our Patreon supporters: Emil Abu Milad, Tj Steyn, meg noah, Bernard McGee, KeyWestr, Amadeo Bee, TTST, Balkrishna Heroor, John H. Austin, Jr., john kiehl, Anton Ragin, Diffbot, Gnare, Dave Kircher, Burt Humburg, Blake Byers, Evgeny Skvortsov, Meekay, Bill Linder, Paul Peijzel, Josh Hibschman, Mac Malkawi, Juan Benet, Ubiquity Ventures, Richard Sundvall, Lee Redden, Stephen Wilcox, Marinus Kuivenhoven, Michael Krugman, Sam Lutfi.
▀▀▀ Written by Casper Mebius, Derek Muller & Petr Lebedev Edited by Trenton Oliver & Jamie MacLeod Animated by Mike Radjabov, Ivy Tello, Fabio Albertelli and Jakub Misiek Filmed by Derek Muller, Albert Leung & Raquel Nuno Molecular collisions video by CSIRO's Data61 via YouTube: Simulation of air Additional video/photos supplied by Getty Images, Pond5 and by courtesy of NASA, NASA's Goddard Space Flight Center, NASA Goddard Flight Lab/ CI Lab, NASA/SDO and the AIA, EVE, HMI, and WMAP science teams. As well as the Advanced Visualization Laboratory at the National Center for Supercomputing Applications, B. Robertson, L. Hernquist Music from Epidemic Sound & Jonny Hyman Produced by Derek Muller, Petr Lebedev, Emily Zhang, & Casper Mebius
[Source](https://www.youtube.com/watch?v=DxL2HoqLbyA)