What is entropy? A measure of just how little we know
Debate over a Quanta Magazine piece on entropy centers on whether entropy is an objective physical property or fundamentally tied to an observer’s knowledge and choice of macroscopic variables. Commenters contrast the thermodynamic view, where entropy is measured via quantities like heat and volume and appears observer‑independent, with information‑theoretic and Jaynes-style interpretations that treat entropy as “missing information” relative to a chosen coarse-graining of microstates. The thread also touches on implications for the arrow of time, Maxwell’s demon, quantum mechanics, and how popular science outlets succeed or fail at conveying these subtleties.
Nature of Entropy: Property of System vs Knowledge
- Strong debate over whether entropy is an objective property of a physical system or a measure of an observer’s ignorance.
- One side: thermodynamic entropy is fixed by the system’s actual microstates and thermodynamic variables; experiments (calorimetry, equations of state) give consistent values independent of what anyone “knows.”
- Other side: entropy is always defined relative to a chosen description (macro-variables, coarse graining); thus it is a property of “system + description,” and in that sense observer- or model-dependent.
Thermodynamics vs Information Theory
- Information theory and Bayesian/statistical perspectives treat entropy explicitly as “missing information.”
- Some argue this view has deep roots (Jaynes, MaxEnt, “anthropomorphic” entropy) and is fruitful, including in quantum statistical mechanics.
- Others warn that importing information-theoretic intuition into thermodynamics can be misleading or unphysical if taken too literally.
Macrostates, Coarse-Graining, and Subjectivity
- Entropy depends on how microstates are grouped into macrostates (e.g., pressure-only vs partial pressures of gas components), so different choices yield different entropies.
- Disagreement: whether this is akin to a coordinate/unit change (trivial, no physical difference) or genuinely different physical descriptions predicting different experimental outcomes.
- Several examples with gas mixtures, distinguishable vs indistinguishable particles, and the Gibbs paradox are used to argue both sides.
Probability, Quantum Mechanics, and Ignorance
- One camp: probabilities reflect only lack of knowledge; calling them “properties of systems” is a mind projection error.
- Counterpoint: quantum measurement outcomes are fundamentally probabilistic within known limits; even a maximally informed observer can only assign probabilities, so some probabilities are taken as objective features of physical setups.
Temperature, Second Law, and Work Extraction
- Temperature and entropy are tightly linked; if entropy is observer-relative, temperature may be as well.
- Others insist that everyday thermodynamic phenomena (ice melting, heat engines, no perpetual motion) are observer-independent, constraining any subjective interpretation.
- Work extractable from a system can depend on what macro-variables you can control and measure, reinforcing a “capabilities-relative” notion of entropy.
Article Style, Interactives, and Side Topics
- Many praise the explorable, interactive format; some mention “explorable explanations” and related terminology.
- Some criticize the article as muddled or lifestyle-ish compared to more concise treatments.
- Minor side threads touch on sci-fi references, cosmology (heat death, Big Bang, ToE, chaos), and implementation details of the interactives (Svelte, iframes).