Science › Classical physics
Entropy: disorder always grows
1865· Idea
ProvenTested many times; part of working physics.
A measure of disorder, more precisely of how many ways a system's parts can be arranged; in isolation it never decreases.
See it on the Science map →How it works
Rudolf Clausius coined the word in 1865. Hot coffee cools, ice melts, buildings decay, and none of it spontaneously reverses. Boltzmann explained why: disordered arrangements vastly outnumber ordered ones, so random jostling almost always moves toward disorder. Order can grow locally, as in a living cell or a freezer, but only by exporting more disorder, usually as waste heat, to the surroundings.
Why it matters
It explains why engines waste heat, why processes run one way, and arguably why time has a direction at all.
Think of it like
A building left unmanaged drifts toward disrepair. Keeping it orderly takes constant maintenance, and that effort creates waste and disorder elsewhere.
How we know
Every heat-engine measurement since the 1800s; chemistry and materials science rely on it daily. Experiments since 2002 confirm that tiny systems briefly run 'backward' as often as statistical physics predicts.
Still a mystery
Why the universe began in a state of extraordinarily low entropy is unexplained; that starting condition is what gives everything since its direction.
Connections (10)
▸Thermodynamics: energy and heat introduced Entropy: disorder always growsProven
The relationship
Studying why no engine can turn all its heat into work, Clausius defined a quantity, entropy, that measures how spread out heat energy has become. The second law says it never decreases in an isolated system. That one rule explains why heat flows from hot to cold and sets the maximum efficiency of every engine.
How the link was found
Sadi Carnot's 1824 engine analysis laid the groundwork. Rudolf Clausius coined 'entropy' in 1865, from the Greek for transformation.
Why it's proven
Every measured heat engine, refrigerator and chemical reaction obeys it. No exception has ever been seen in a large system.
Open questions and mysteries
Thermodynamics alone says entropy grows but not why. Boltzmann's statistics explained it, but the universe's low-entropy starting point remains unexplained.
▸Ludwig Boltzmann gave a counting formula for Entropy: disorder always growsProven
The relationship
Boltzmann showed that entropy counts the number of microscopic arrangements of atoms that look identical from outside. Because disordered arrangements vastly outnumber ordered ones, random motion almost always moves a system toward higher entropy. The second law became a statement of overwhelming probability rather than an absolute command.
How the link was found
Boltzmann, in papers from 1872 and especially 1877. Max Planck wrote the formula in its famous form, S = k log W, around 1900.
Why it's proven
Statistical predictions match measured heat capacities and gas properties. Small-scale experiments since 2002 see brief entropy decreases at exactly the predicted rates.
Open questions and mysteries
Why the universe started with low entropy, which Boltzmann himself puzzled over, remains open.
▸Probability lets Boltzmann count states for Entropy: disorder always growsProven
The relationship
Boltzmann couldn't track trillions of molecules individually, so he used probability to ask which overall states are most likely. Entropy became a measure of likelihood: the more ways to arrange the atoms for a given state, the more probable that state. Probability turned thermodynamics' unexplained rule into a near-certain statistical outcome.
How the link was found
Maxwell brought probability into gas theory in 1860; Boltzmann extended it to entropy in 1872–1877; Josiah Willard Gibbs generalised it in 1902.
Why it's proven
Statistical mechanics accurately predicts measured properties of gases, solids and radiation, and small-scale fluctuation experiments match the predicted probabilities.
Open questions and mysteries
Whether these probabilities reflect our ignorance of atomic details or something objective about nature is still debated by philosophers of physics.
▸Entropy: disorder always grows explains The arrow of timeWell supported
The relationship
The fundamental laws work the same forward and backward, but entropy rises in only one direction. That rise distinguishes past from future: eggs break, heat spreads, records form. If entropy began very low at the Big Bang and has climbed ever since, the direction of time we experience follows from that slope.
How the link was found
Boltzmann argued this in the 1870s–1890s. Arthur Eddington coined 'arrow of time' in his 1927 lectures, published in 1928.
Is it proven?
Well supported: every irreversible process tracks rising entropy. Not fully proven, because the explanation depends on an unexplained low-entropy beginning.
Open questions and mysteries
Why the Big Bang was so ordered, and whether our sense of time's flow, memory and causation all reduce to entropy.
▸Entropy: disorder always grows is really missing information, linking to Information is physicalProven
The relationship
Entropy measures how many microscopic arrangements fit what we see in bulk. That is the same as how much information we lack about the exact arrangement. Treating entropy as missing information means information must obey thermodynamics too: erasing a bit raises the entropy of the surroundings, which is exactly Landauer's rule that information is physical.
How the link was found
Ludwig Boltzmann's 1870s entropy formula and Claude Shannon's 1948 information formula turned out to match. Leo Szilard (1929) and Rolf Landauer (1961) connected them to heat, and Charles Bennett (1982) used the link to defeat Maxwell's demon.
Why it's proven
The math is exact. In 2012 Bérut and colleagues measured the heat from erasing one bit, approaching Landauer's minimum. Earlier, in 2010, Toyabe and colleagues converted information into usable work in a lab.
Open questions and mysteries
Whether entropy is purely about our knowledge or an objective property of the world is still argued by philosophers of physics.
▸Black-hole entropy: information on the surface is the black-hole version of Entropy: disorder always growsWell supported
The relationship
Ordinary entropy counts how many internal arrangements match what we see. Black-hole entropy applies the same accounting to black holes and folds them into the second law: ordinary entropy plus black-hole entropy never goes down. Black holes turn out to be enormous entropy stores. The Milky Way's central black hole holds far more entropy than all its stars combined.
How the link was found
Bekenstein (1972) proposed it; Bardeen, Carter and Hawking (1973) set out the four "laws of black hole mechanics" that mirror thermodynamics; Hawking's 1974 result made the match exact.
Is it proven?
The mathematics is consistent, and the 1996 string-theory count matched it. LIGO's horizon-area tests (2021, 2025) support the black-hole second law.
Open questions and mysteries
Ordinary entropy counts atoms. What are the "atoms" of a black hole?
▸Information theory (Shannon) uses the same formula as Entropy: disorder always growsProven
The relationship
Shannon's measure of a message's average information has the same mathematical form as the entropy of Gibbs and Boltzmann: both add up probabilities weighted by their logarithms. Thermodynamic entropy can be read as the missing information about which exact microscopic arrangement a system is in. On this view heat and information are two faces of one quantity.
How the link was found
Shannon noticed the shared formula in 1948; Edwin Jaynes rebuilt statistical mechanics on information theory in 1957; Rolf Landauer linked erasing information to heat in 1961.
Why it's proven
The formulas are mathematically identical. Landauer's predicted heat from erasing one bit was measured in 2012 by Antoine Bérut and colleagues.
Open questions and mysteries
Whether thermodynamic entropy is fundamentally about information (an observer's knowledge) or about physical states alone is still debated.
▸Claude Shannon borrowed the name and formula of Entropy: disorder always growsProven
The relationship
Shannon's measure of the uncertainty in a message had the same mathematical form as Gibbs's entropy in statistical mechanics. He called it entropy, reportedly on John von Neumann's advice. The shared name stuck, and encouraged physicists to read thermodynamic entropy as missing information.
How the link was found
Shannon, 1948. The von Neumann story comes from a 1971 account by Myron Tribus; it is often repeated but not fully verified.
Why it's proven
The formulas match exactly. The physical link between information and heat was confirmed by 2012 measurements of Landauer's principle.
Open questions and mysteries
Whether the two entropies are the same physical thing or merely share mathematics is still argued.
▸Cyclic universes (ekpyrotic and Penrose's CCC) must explain the reset of Entropy: disorder always growsOpen question
The relationship
Entropy only grows, so each cycle should start more disordered than the last, and cycles would grow longer and larger. Run backward, that implies a first cycle, defeating the point. The ekpyrotic answer: each cycle's expansion spreads entropy so thin that any observable region starts fresh. Penrose argues entropy is effectively reset as black holes evaporate and scale disappears.
How the link was found
Richard Tolman identified the problem for oscillating universes in 1931–34. Steinhardt and Turok (2002) and Penrose (from 2005) proposed their resets in response.
Is it proven?
Neither reset is accepted. The ekpyrotic dilution is calculated within its model; Penrose's relies on information being destroyed in black holes, which most physicists now doubt.
Open questions and mysteries
Why was our Big Bang so low in entropy? Every cyclic model must answer that, and none has convinced most cosmologists.
▸Entropy: disorder always grows points toward heat death in How the universe endsWell supported
The relationship
Total entropy keeps rising. Stars, weather and life all run on flows from hot to cold and from ordered to disordered energy. In an ever-expanding universe those differences eventually run out: stars burn out, black holes evaporate into faint radiation, and everything approaches the same near-zero temperature. With no differences left, nothing more can happen. That end state is the heat death.
How the link was found
William Thomson (later Lord Kelvin) argued in 1852 that the dissipation of energy would eventually leave the world unable to support life. Hermann von Helmholtz extended the idea to the whole universe in an 1854 lecture.
Is it proven?
The second law is among the most tested ideas in physics. Applying it to the whole universe, with gravity and expansion included, is reasonable but uncertain, because gravitating systems behave unusually.
Open questions and mysteries
Could rare random fluctuations in an endless, maximum-entropy universe create new structure, or even new universes? The 'Boltzmann brain' puzzle, about lone minds born from such fluctuations, hinges on this.