science

The Laws of Thermodynamics

Four rules that nothing escapes, told as one story about energy, statistics and time.

The laws of thermodynamics are four rules for energy and heat. The zeroth law says that two systems each in thermal equilibrium with a third are in equilibrium with each other, which is what makes temperature meaningful. The first says energy is conserved. The second says the entropy of an isolated system doesn't decrease. The third says entropy approaches a minimum as temperature approaches absolute zero, which can't be reached in a finite number of steps.

Four rules nothing escapes

Thermodynamics began, as Richard Feynman put it, with "an analysis, by the great engineer Sadi Carnot, of the problem of how to build the best and most efficient engine". Feynman called it one of the few famous cases in which engineering contributed fundamentally to physical theory (Feynman Lectures, Vol. I, ch. 44). Carnot wanted better steam engines. What came out of that work were rules that apply to stars, cells, refrigerators and computers alike.

The history runs out of order. Carnot found the essence of the second law before anyone had stated the first (Feynman, ch. 44). Rudolf Clausius named entropy in 1865 (Wikipedia). Walther Nernst developed the third law between 1906 and 1912 (Wikipedia). And the law that logically comes first was only set down in the 1930s, which is why it carries the awkward number zero.

The four laws at a glance

Law	Plain statement	What it rules out	Who and when
Zeroth	If A and B are each in thermal equilibrium with C, they are in equilibrium with each other	Temperature being meaningless from one object to the next	Ralph H. Fowler, 1930s
First	Energy is conserved: the change in internal energy equals heat added plus work done on the system	Perpetual motion of the first kind: work from nothing	Stated after Carnot's work on engines
Second	The entropy of an isolated system never decreases; no process can turn heat from a single reservoir entirely into work	Perpetual motion of the second kind; heat flowing by itself from cold to hot	Carnot (engines), Clausius (entropy, 1865)
Third	Entropy approaches a minimum as temperature approaches absolute zero	Reaching absolute zero in a finite number of steps	Walther Nernst, 1906 to 1912

Sources for the table: Feynman, ch. 44; Wikipedia on the zeroth law, third law and perpetual motion.

Why is there a zeroth law?

The zeroth law sounds too obvious to need saying. If your coffee is the same temperature as a thermometer, and the thermometer is the same temperature as your tea, then the coffee and the tea are the same temperature.

But "obvious" isn't "guaranteed". This transitivity is exactly what lets a thermometer work: it is what makes temperature a single number you can compare across objects that have never touched. The zeroth law is needed to define temperature scales at all, and it justifies the use of practical thermometers (Wikipedia).

It was stated last. The law "was established by Ralph H. Fowler in the 1930s, long after the first, second, and third laws had been widely recognized" (Wikipedia). Since the other three already depended on it, it couldn't be the fourth, so it became the zeroth. The zeroth law essay goes further into why something so simple carries so much weight.

The first law: energy bookkeeping

The first law is conservation of energy, written for heat. In Feynman's version: the heat put into a system plus the work done on it equals the increase in its internal energy, ΔU = Q + W (Feynman, ch. 44). (Some textbooks count work done by the system and write ΔU = Q − W. It's the same law with a different sign convention.)

Energy changes form. It doesn't appear or vanish. That rules out a perpetual motion machine of the first kind, one that "produces work without the input of energy" (Wikipedia). Every such design has to hide an energy source somewhere, or fail. The first law essay follows the accounting through engines and living things.

What the first law doesn't tell you is which way things go. A ball falling and a ball rising conserve energy equally well. For direction, you need the second law.

The second law: why some things only go one way

Feynman states the second law in Carnot's form: "A process whose only net result is to take heat from a reservoir and convert it to work is impossible." He shows that this is equivalent to the familiar version: heat cannot, of itself, flow from a cold object to a hot one (Feynman, ch. 44). In terms of entropy: in a reversible change the total entropy of everything involved stays the same, and in any irreversible change it increases. Since no real process is perfectly reversible, there is always some gain.

That rules out perpetual motion of the second kind: a machine that would run by spontaneously cooling a single heat reservoir, the ocean, say, and turning that heat into work (Wikipedia). Such a machine would conserve energy perfectly and still be impossible. It also caps every engine. Feynman derives the limit for an ideal engine running between a hot temperature T₁ and a cold one T₂: efficiency = (T₁ − T₂)/T₁, which is always less than one (ch. 44). Carnot's engines and their limit are covered in the second law essay.

This is also the law with an arrow. Hot coffee cools; a cool cup never spontaneously heats up while the room gets colder. What entropy actually measures, and why "disorder" is a poor translation, is the subject of What Is Entropy, Really? The Second Law Without the 'Disorder' Myth.

Can a clever enough being cheat? James Clerk Maxwell imagined one in 1867: a tiny gatekeeper sorting fast molecules from slow ones (Wikipedia). It took more than a century of argument to show why it can't beat the second law, and the answer turned out to be about information. That story is in Maxwell's Demon.

The third law: the unreachable floor

For a long time, Feynman notes, it was believed that only differences in entropy meant anything. Then Nernst proposed his heat theorem, which became the third law: the entropy of an object at absolute zero is zero (Feynman, ch. 44). That gave entropy an absolute starting point.

Modern statements are more careful. Planck's version applies to perfect crystals, whose entropy tends to a constant that can be set to zero. Nernst's unattainability principle says that no process, however idealized, can reduce a system's entropy to its absolute-zero value "in a finite number of operations" (Wikipedia). Every step closer gets harder.

You can still get remarkably close. In 2018, researchers at the University of Bremen reached 38 picokelvin, 38 trillionths of a degree above absolute zero (Wikipedia). Close, but not there. The third law essay explains why the floor stays locked.

Can the laws be broken?

Not in any confirmed case at macroscopic scales. The second law is the subtle one: it is statistical. Ludwig Boltzmann's formula, S = k ln W, which ties entropy to the number of microscopic arrangements W that match what you see, was first formulated between 1872 and 1875 and is carved on his gravestone in Vienna (Wikipedia). On that view, entropy decreases aren't strictly forbidden, just overwhelmingly improbable for systems with enormous numbers of particles. At the scale of a few molecules, small fluctuations do happen. At the scale of a coffee cup, you will never see one.

Why they're really one story

Each law can be read as one face of the same picture: matter made of huge numbers of particles, with energy shared among them.

The zeroth law says there is a single quantity, temperature, that equalizes when energy can flow. The first says the total energy is fixed. The second says that energy spreads into the arrangements that are most numerous, because there are vastly more of them. The third says that at the bottom of the temperature scale, the number of available arrangements shrinks toward its minimum. Statistical mechanics, which Boltzmann helped found, is the theory that connects the counting of arrangements to the measurable quantities of heat and temperature.

That is also why life doesn't break the second law. A living thing is not an isolated system. It takes in energy and matter and gives off heat and waste, so the entropy of the organism plus its surroundings still rises. Erwin Schrödinger, in his 1944 book What Is Life?, first said that life "feeds on negative entropy", then corrected himself in a later edition: the true source is free energy (Wikipedia). Because life on Earth runs at roughly constant temperature and pressure, the relevant quantity is Gibbs free energy, the subject of another series on this site.

The series

The Laws of Thermodynamics (this page)
The Zeroth Law: Why Temperature Makes Sense
The First Law: Energy Conservation
The Second Law: Entropy Always Increases (including Carnot and heat engines)
The Third Law: You Can't Reach Absolute Zero
What Is Entropy, Really? The Second Law Without the 'Disorder' Myth
Maxwell's Demon: Information and Thermodynamics
Synthesis: Why These Four Laws Rule Everything

The short version

Temperature is comparable, energy is conserved, entropy only climbs in isolation, and absolute zero is a limit rather than a destination. Carnot's question about steam engines turned out to be a question about everything made of many parts.

The pebble: energy is never lost, only spread out, and everything interesting happens while it spreads.

FAQ

What are the four laws of thermodynamics in simple terms?

Zeroth: things in thermal equilibrium with the same third thing share a temperature. First: energy can't be created or destroyed. Second: the entropy of an isolated system never decreases, so heat won't flow from cold to hot by itself. Third: you can approach absolute zero but never reach it in a finite number of steps.

Why is it called the zeroth law?

Because it was stated last but is logically first. Ralph H. Fowler established it in the 1930s, after the first, second and third laws were already named, and the others rely on it to define temperature.

Can the laws of thermodynamics be broken?

There is no confirmed violation at macroscopic scales. The second law is statistical, so tiny, brief entropy decreases can occur in systems of a few molecules, but for anything you can see they are so improbable that they don't happen.

Does life violate the second law?

No. Living things are open systems. They take in free energy (from food or sunlight) and release heat and waste, so the total entropy of the organism plus its surroundings still increases.

Why can't we reach absolute zero?

Nernst's unattainability principle says no process can bring a system's entropy to its absolute-zero value in a finite number of operations. Each step of cooling achieves less than the one before. The record is 38 picokelvin, set in 2018.