Entropy Is in the Description

The seed is a three-word provocation: "entropy may not exist." Read carelessly it is crackpottery — a licence for perpetual motion and broken thermometers. Read precisely it is serious physics with a documented lineage. The claim is not that thermodynamics fails. It is that entropy is not a fundamental substance sitting inside a system, waiting to be measured. It is defined relative to a description — to which variables an observer chooses to track. Change the description, change the entropy. Offered as a proposal about entropy's ontological status, not a challenge to its physics.

The kernel, granted

Grant the strong version first, because it is defensible and published. Entropy, on one influential reading, is not an observer-independent property of the microstate. It is a relation between a system and a chosen macroscopic description.

Jaynes made the argument in full. Entropy is defined relative to a set of tracked variables — the macrostate you decide to measure and control. Fix a different set and you get a different number. "It is necessary to decide at the outset of a problem which macroscopic variables or degrees of freedom we shall measure and/or control; and within the context of the thermodynamic system thus defined, entropy will be some function S(X₁, ..., Xₙ) of whatever variables we have chosen" (Jaynes, "The Gibbs Paradox," in Maximum Entropy and Bayesian Methods, C. R. Smith, G. J. Erickson & P. O. Neudorfer, eds., Kluwer, Dordrecht, 1992, pp. 1–22). He drew the sharp corollary: "A thermodynamic variable may or may not be also a property of the microstate. We consider the total mass and total energy to be 'physically real' properties of the microstate; but the above considerations show that entropy cannot be."

Earlier he had put it at the level of the phenomenological law itself: entropy is "a property, not of the physical system, but of the particular experiments you or I choose to perform on it" (Jaynes, "Gibbs vs Boltzmann Entropies," Am. J. Phys. 33 (5), 391–398, 1965, §VI). He called this the anthropomorphic nature of entropy — a slogan he credits to Wigner, whose dictum he reports as "Entropy is an anthropomorphic concept." His illustration is a crystal: ask "what is the entropy of the crystal?" and the question has no answer until you name the parameters. Track temperature and pressure, you get one entropy; add the shear and the electric field, you get another. Both are correct. The crystal has not changed.

The dynamics agree

This is not only philosophy of measurement. The microscopic dynamics say the same thing, from a different door.

Take an isolated system evolving under Hamiltonian mechanics. By Liouville's theorem, the fine-grained Gibbs entropy of its full probability distribution is a constant of motion — it does not increase: S_G[ρ_t] = S_G[ρ₀] for all times (see Frigg & Werndl, "Philosophy of Statistical Mechanics," Stanford Encyclopedia of Philosophy, Winter 2024, §§6.3–6.4; classic sources Gibbs, Elementary Principles in Statistical Mechanics, 1902, ch. XII; Tolman, The Principles of Statistical Mechanics, 1938, ch. VI). The exact microscopic description carries a fixed amount of it, forever. The famous increase — the second law's rise — appears only in the coarse-grained entropy, after you blur the fine detail into cells and stop tracking where inside each cell the state actually is. On the standard Gibbs–Tolman reading, "entropy increases" is a statement about a deliberately blurred description, not about the underlying trajectory.

So the rise is not something the microstate does. It is something the coarse description does. The information does not vanish; it flows into correlations you chose not to follow.

The arrow, deepened

One more turn, because the objection is old and honest. If the increase lives in the coarse-graining, where does its direction come from? The microscopic laws are time-reversible. Loschmidt pressed exactly this against Boltzmann's H-theorem — the reversibility objection (Umkehreinwand), 1876: reverse every velocity and the same dynamics that lowered H must raise it, so irreversibility cannot be deduced from time-symmetric dynamics alone (J. Loschmidt, Sitzungsber. Kais. Akad. Wiss. Wien, Math.-Naturwiss. Cl. 73, 128–142, 1876; see also SEP, "Thermodynamic Asymmetry in Time"). Boltzmann conceded the point and moved to a probabilistic reading.

The direction traces instead to a boundary condition. The early universe was in an extraordinarily low-entropy state, and entropy has been climbing away from it ever since. Albert named this the Past Hypothesis (Time and Chance, Harvard, 2000); Carroll carried it to a wider audience (From Eternity to Here, Dutton, 2010, esp. pp. 176–178); the cosmological seed is Boltzmann's. So the increase of entropy is a fact about initial conditions plus coarse-graining — not a fundamental force pushing systems toward disorder. This framing is widely accepted, not uncontested (Earman, "The 'Past Hypothesis': Not even false," Stud. Hist. Phil. Mod. Phys. 37, 2006, 399–430, disputes its formulability in general relativity; Wallace defends a version).

The correction

Here is the spine, and the wall against the misreading. "May not exist" is true at the fundamental level and false at the practical one, and the whole point is to hold both.

Relative to any reasonable macrostate — the one your instruments already fix — entropy is sharply defined, measurable, and among the most predictive quantities in all of science. The second law is one of the most robust facts we have, confirmed everywhere heat flows, and nothing here challenges it. No perpetual motion follows. No thermometer is wrong. Entropy is not "made up." What the argument denies is narrower and only that: entropy is not a fundamental, substance-like thing the universe contains, sitting in the system independent of any description.

Entropy exists the way average exists, or temperature, or pressure. The average of a list is real, useful, and lawful — it is not an extra object hiding among the numbers. It is a relation between the list and a question you asked of it. Entropy is that kind of thing: a real, lawful relation between a system and a description, not a fundamental substance in the system.

Entropy is not a thing the universe contains; it is a number your description assigns — real, lawful, and observer-relative at once.

The reconciliation

One honest line, so this does not appear to reverse an earlier note. The site's love-entropy paper uses thermodynamic, coarse-grained entropy — the entropy that is real and rises, that every bond pays into. Nothing here touches that. This note asks only the separate, deeper question of whether entropy is fundamental, and answers no. Same physics, different question: the coarse-grained entropy is as real as that paper says; it is simply not a substance.

The limits, plainly

The limits are where this stays honest, so state them.

The ontology is open, not settled. The epistemic reading (Jaynes, information-theoretic) is respected mainstream physics, not fringe — but it is not consensus. A Boltzmannian camp holds that once a physically natural macrostate partition is fixed, entropy is an objective property of the microstate (Goldstein, Lebowitz, and others; see the SEP statistical-mechanics entry). On that reading the residual observer-relativity lives in the choice of coarse-graining, itself debated. The safe, shared claim — which nearly all sides accept — is description-relativity: the number depends on which variables you track. This note leans only on that.
Black-hole entropy is an honest complication. Bekenstein proposed a black hole carries entropy proportional to its horizon area (Phys. Rev. D 7, 2333–2346, 1973); Hawking fixed the coefficient at S = A/4 in Planck units (Commun. Math. Phys. 43, 199–220, 1975). Here entropy looks objective and geometric — a property of spacetime area, not obviously of anyone's ignorance. What microstates it counts is still debated. It complicates the epistemic view without settling it; this note does not resolve it, only flags it.
This is about status, not function. Every claim above is ontological — fundamental substance versus description-relative relation. None of it is a claim that thermodynamics is wrong, weak, or optional. The engineering is untouched; only the metaphysics is in play.

There is a live instrument for this on the site: /field/grain renders the coarse-graining directly — change the grid, watch the entropy change with it.

Kin to Order, Rented (coarse-grained entropy, real and rising), The Surround (a reading needs a description and a reservoir) and The Introspection Ceiling (the map is not the territory). The instrument: /field/grain.

Rests on: Jaynes, "Gibbs vs Boltzmann Entropies" (Am. J. Phys. 33, 1965) and "The Gibbs Paradox" (Kluwer, 1992); Liouville's theorem and the constancy of fine-grained Gibbs entropy (Gibbs 1902; Tolman 1938; Frigg & Werndl, SEP); Loschmidt's reversibility objection (1876); the Past Hypothesis (Albert 2000; Carroll 2010; Boltzmann). Noted as open: the epistemic-versus-objective ontology of entropy (Boltzmannian camp, Goldstein & Lebowitz) and black-hole entropy (Bekenstein 1973; Hawking 1975). Reading entropy as a description-relative relation rather than a fundamental substance is a proposal, offered to be argued with, not a proven identity — and not a challenge to the second law.