Why Does Time Only Go Forward? Entropy and the Arrow of Time

Film a pair of billiard balls colliding and run the clip backwards: it still looks like physics. Film an egg hitting the floor and run it backwards, and everyone laughs. The laws governing individual particles barely care which way time runs, yet the world around us has an unmistakable direction. Physicists call this the arrow of time. Its best-understood source is entropy, the quantity our Entropy Warden enforces.

What is the arrow of time?

The phrase was coined by the astronomer Arthur Eddington, who connected it to the growth of randomness in the world. Quanta Magazine’s history of time, by Dan Falk, recounts that origin and Stephen Hawking’s later distinction between three arrows: psychological (we remember the past, not the future), thermodynamic (entropy increases) and cosmological (the universe expands) (Quanta^[1]). Of the three, the thermodynamic arrow is the one physics can say the most about.

What is entropy, in plain words?

Rudolf Clausius introduced the word “entropy” in 1865 while formalising the second law of thermodynamics (Britannica^[2]). In thermodynamics, a change in entropy is heat transferred divided by temperature: ΔS = Q/T for a reversible process. Feynman’s lecture on the laws of thermodynamics develops it from Carnot’s ideal heat engine (Feynman Lectures I-44^[3]).

Ludwig Boltzmann gave entropy its statistical meaning: S = k ln W, where W counts the number of microscopic arrangements consistent with what you see on the large scale, and k is Boltzmann’s constant. Since the 2019 SI revision, k is fixed at exactly 1.380 649 × 10⁻²³ J/K (NIST^[4]). A shuffled deck, a mixed cup of coffee, a gas filling a room: these are states with vastly more arrangements than their tidy alternatives. That is what our Boltzmann sticker means by “there are more ways to be a mess.”

What does the second law say exactly?

For an isolated system, entropy does not decrease: ΔS ≥ 0. Two qualifications matter. First, “isolated” is essential; a fridge lowers the entropy inside it by raising it outside by more. Second, the law is statistical. A decrease is not forbidden by the equations of motion; it is just overwhelmingly improbable for anything large. Our house phrase is “statistics, not prohibition.”

Why does entropy increase?

Because high-entropy states vastly outnumber low-entropy ones. If a system starts in a rare, ordered macrostate and wanders through its possible microstates, it will almost certainly end up in one of the overwhelmingly common disordered ones. Run the same reasoning backwards, though, and it predicts that entropy was higher in the past too. Something has to break the tie.

Why was the past special? The Past Hypothesis

The usual answer is that the universe began in a state of very low entropy, and has been running “downhill” ever since. Philosophers of physics call this assumption the Past Hypothesis; the Stanford Encyclopedia of Philosophy’s entry on thermodynamic asymmetry in time discusses it in detail, along with the objections (SEP^[5]). Philip Ball, writing in Quanta, puts the standard view plainly: the universe began, “for reasons not fully understood or agreed on,” in a low-entropy state and is heading toward one of ever higher entropy (Quanta^[6]).

Why the early universe had such low entropy is an open question. The hot, smooth early cosmos may look “disordered,” but once gravity is taken into account, a smooth distribution of matter is a highly special, low-entropy state; gravity makes clumping the likely direction. Explaining that starting point is one of the deep unsolved problems of cosmology.

Will the universe end in heat death?

If entropy keeps rising, eventually there will be no temperature differences left to drive engines, stars or life. Nineteenth-century physicists called this the heat death of the universe, as Ball’s article notes (Quanta^[6]). Our Entropy Echo tee is that slow fade. It is a projection based on known physics, not a certainty: it depends on the long-term behaviour of dark energy and on physics we do not yet fully understand. For the cosmology side, see our Void Whisperer design.

Can Maxwell’s demon beat the second law?

James Clerk Maxwell imagined a tiny being who opens a trapdoor between two boxes of gas, letting only fast molecules through one way. The gas would separate into hot and cold without any work being done, apparently lowering entropy (Britannica^[7]). Our sticker Sortex is that demon.

The modern resolution involves information. In 1961 Rolf Landauer argued (IBM J. Res. Dev.^[8]) that erasing one bit of information in an environment at temperature T must dissipate at least kT ln 2 of heat. In 2012, Antoine Bérut and colleagues reported in Nature an experiment with a colloidal particle in a double-well trap, showing that the mean dissipated heat approached the Landauer bound in the limit of slow erasure (Nature^[9]). The demon has to record and eventually erase what it knows, and that bookkeeping costs at least as much entropy as it saves.

Is that the complete exorcism? Here the experts genuinely disagree. Some argue that Landauer’s principle is the key; others, such as the philosopher of physics John Norton, have argued that the standard arguments for it are circular or incomplete (Norton 2011^[10]). We label this one open, as we do on the Sortex sticker.

Does quantum mechanics change the story?

Some recent work traces the rise of entropy to quantum entanglement: as a system interacts with its surroundings, information about it spreads into correlations that are, in practice, impossible to gather back. Ball’s 2022 Quanta article describes one such programme by Carlo Maria Scandolo and Giulio Chiribella, which derives entropy-like constraints from axioms about information (Quanta^[6]). This links the thermodynamic arrow to decoherence, which we discuss in What Is Quantum Measurement, Really? Whether the quantum and thermodynamic arrows are ultimately the same thing remains under active research.

Can temperature be negative?

Strangely, yes, in a specific technical sense. For systems with a maximum possible energy, such as a set of nuclear spins in a magnetic field, you can put more particles in the upper level than the lower one. With the Boltzmann definition of temperature, that population inversion corresponds to a negative absolute temperature, which is “hotter” than any positive one: heat flows from it to any positive-temperature system. Our sticker Invertia explains the 1951 Purcell–Pound experiment on nuclear spins in a lithium fluoride crystal (Phys. Rev.^[11]). Whether this is the right definition of temperature for such systems is debated; Jörn Dunkel and Stefan Hilbert argued in 2014 for an alternative (Gibbs) definition of entropy under which these temperatures are not negative (Nature Physics^[12]), and others have defended the Boltzmann version (Am. J. Phys.^[13]). We cover it more in What Happens at Absolute Zero?

Why do we remember the past and not the future?

A memory is a physical record, and making records generally increases entropy. Many physicists and philosophers argue that the psychological arrow therefore piggy-backs on the thermodynamic one, which is why the SEP entry treats “the direction of time” and thermodynamic asymmetry together (SEP^[5]). This is an argument, not a theorem, but it is the most widely discussed one.

Common misconceptions

• “Entropy is just disorder.” Disorder is a useful picture, but the precise meaning is the count of microstates (or heat over temperature). Some ordered-looking things, like crystals forming in a cooling liquid, increase total entropy because they release heat.
• “Life violates the second law.” Living things are not isolated systems. They lower their own entropy by raising their surroundings’ more, mostly by radiating heat.
• “The second law is absolute.” It is statistical. For small systems, short-lived entropy decreases do happen; for anything human-sized they are so improbable that they never matter.

Key terms in plain English

• Microstate: one exact arrangement of every particle’s position and motion.
• Macrostate: what you can see on the large scale, such as temperature, pressure and volume. Many microstates share one macrostate.
• Entropy: in Boltzmann’s form, S = k ln W, where W counts the microstates behind a macrostate (NIST^[4]).
• Isolated system: one that exchanges neither energy nor matter with its surroundings. The second law’s ΔS ≥ 0 is stated for these.
• Equilibrium: the macrostate a system settles into, the one with the most microstates for its energy.
• Reversible process: an idealised, infinitely slow change in which total entropy stays constant. Real processes are irreversible and increase it (Feynman Lectures^[3]).

Is the second law ever broken?

For anything you can see, no. But because the law is statistical, very small systems observed over very short times do sometimes show brief decreases in entropy, and modern experiments with microscopic beads and molecules study exactly these fluctuations. The Landauer experiment described above used a single colloidal particle for this reason: at that scale, thermal jiggling is large enough that heat and information can be measured almost bit by bit (Nature^[9]). Over many repetitions, the average still obeys the second law. That is what “statistics, not prohibition” means in practice: individual surprises are allowed; systematic ones are not.

Is time itself asymmetric?

Most of the fundamental equations of physics are, to a very good approximation, the same run forwards or backwards. The SEP entry surveys attempts to locate the direction of time in cosmology, in quantum mechanics, in causation, and in time itself, and none has displaced the low-entropy past as the standard explanation (SEP^[5]).

A short timeline of the arrow of time

• 1865: Rudolf Clausius names entropy and states that the entropy of the universe tends to a maximum (Britannica^[2]).
• 1870s: Ludwig Boltzmann connects entropy to the counting of microscopic arrangements, the idea behind S = k ln W.
• 1920s: Arthur Eddington coins the phrase “arrow of time” (Quanta^[1]).
• 1961: Rolf Landauer argues that erasing information has a minimum heat cost (IBM J. Res. Dev.^[8]).
• 2012: Bérut and colleagues measure heat dissipation approaching the Landauer bound (Nature^[9]).
• Today: the low-entropy origin of the universe remains the main open question (SEP^[5]).

The bottom line

Time’s arrow is not written into the basic laws of motion. It comes from probability plus a special starting point: disordered states vastly outnumber ordered ones, and the universe began in an extraordinarily ordered one. Everything else, from melting ice to memory, follows from that combination. What made the beginning so special is still open.

FAQ

What is the second law of thermodynamics in one sentence?

The entropy of an isolated system does not decrease, as a matter of overwhelming statistical likelihood (Feynman Lectures^[3]).

Who discovered entropy?

Rudolf Clausius named and defined it in 1865 (Britannica^[2]); Ludwig Boltzmann gave it its statistical form.

Is the arrow of time fully explained?

Partly. Given a low-entropy past, statistics explains the arrow. Why the past was low-entropy is still open (SEP^[5]).

Does information have a physical cost?

Erasing information has a minimum heat cost of kT ln 2 per bit, approached experimentally in 2012 (Nature^[9]).

See the whole Thermodynamics collection, or the Energy Accounts sticker sheet. For a short refresher, our older post Thermodynamics Made Simple covers the four laws.

References

1. Dan Falk, “Arrows of Time,” Quanta Magazine (2020). https://www.quantamagazine.org/what-is-time-a-history-of-physics-biology-clocks-and-culture-20200504/
2. R. Clausius (1865), Annalen der Physik 201, 353 (the paper that introduced “entropy”). https://doi.org/10.1002/andp.18652010702
3. Feynman Lectures on Physics, Vol. I, Ch. 44: The Laws of Thermodynamics. https://www.feynmanlectures.caltech.edu/I_44.html
4. NIST CODATA, Boltzmann constant. https://physics.nist.gov/cgi-bin/cuu/Value?k
5. Stanford Encyclopedia of Philosophy, “Thermodynamic Asymmetry in Time”. https://plato.stanford.edu/entries/time-thermo/
6. Philip Ball, “Physicists Trace the Rise in Entropy to Quantum Information,” Quanta Magazine (2022). https://www.quantamagazine.org/physicists-trace-the-rise-in-entropy-to-quantum-information-20220526/
7. Encyclopaedia Britannica — Maxwell’s demon. https://www.britannica.com/science/Maxwells-demon
8. Landauer (1961) Irreversibility and Heat Generation in the Computing Process, IBM J. Res. Dev. 5, 183. https://doi.org/10.1147/rd.53.0183
9. Bérut et al. (2012), “Experimental verification of Landauer’s principle linking information and thermodynamics,” Nature 483, 187. https://doi.org/10.1038/nature10872
10. Norton (2011) Waiting for Landauer, Stud. Hist. Phil. Mod. Phys. 42, 184. https://doi.org/10.1016/j.shpsb.2011.05.002
11. Purcell & Pound (1951) A Nuclear Spin System at Negative Temperature, Phys. Rev. 81, 279 (reversed state decayed with the 5-min time constant). https://doi.org/10.1103/PhysRev.81.279
12. Dunkel & Hilbert (2014) Consistent thermostatistics forbids negative absolute temperatures, Nature Phys. 10, 67. https://doi.org/10.1038/nphys2815
13. Frenkel & Warren (2015) Gibbs, Boltzmann, and negative temperatures, Am. J. Phys. 83, 163. https://doi.org/10.1119/1.4895828

Written by Pixelated Physics. Every factual claim is linked to the source we checked; points that are still debated are labelled open.