Quasiclassical Coarse Graining and Thermodynamic Entropy

TL;DR

This work argues that classical physics and thermodynamic entropy emerge in a quantum universe through unavoidable coarse graining of histories. By focusing on quasiclassical realms—decoherent coarse grainings built from averages of conserved-density variables—the authors derive approximate classical dynamics via local equilibrium and connect this to the familiar thermodynamic entropy. They show that completely fine-grained histories cannot decohere nontrivially, justify the central role of coarse graining, and link the quasiclassical entropy to the second law under plausible cosmological initial conditions. The framework unifies quantum cosmology with classical behavior and thermodynamics, and recasts measurement as a subset of decoherent histories rather than a fundamental postulate. Overall, the paper provides a principled account of how the observable, irreversible classical world arises from an underlying quantum closed system.

Abstract

Our everyday descriptions of the universe are highly coarse-grained, following only a tiny fraction of the variables necessary for a perfectly fine-grained description. Coarse graining in classical physics is made natural by our limited powers of observation and computation. But in the modern quantum mechanics of closed systems, some measure of coarse graining is inescapable because there are no non-trivial, probabilistic, fine-grained descriptions. This essay explores the consequences of that fact. Quantum theory allows for various coarse-grained descriptions some of which are mutually incompatible. For most purposes, however, we are interested in the small subset of ``quasiclassical descriptions'' defined by ranges of values of averages over small volumes of densities of conserved quantities such as energy and momentum and approximately conserved quantities such as baryon number. The near-conservation of these quasiclassical quantities results in approximate decoherence, predictability, and local equilibrium, leading to closed sets of equations of motion. In any description, information is sacrificed through the coarse graining that yields decoherence and gives rise to probabilities for histories. In quasiclassical descriptions, further information is sacrificed in exhibiting the emergent regularities summarized by classical equations of motion. An appropriate entropy measures the loss of information. For a ``quasiclassical realm'' this is connected with the usual thermodynamic entropy as obtained from statistical mechanics. It was low for the initial state of our universe and has been increasing since.