The dynamic origin of increasing entropy

TLDR

Thermodynamic states are assumed to be characterized by densities, yet because all physical laws are reversible dynamical systems, it is unclear why entropy tends to a maximum. The study uses recent ergodic‑theory results on density evolution to provide a unified treatment of the origin of classical nonequilibrium thermodynamic behavior. The authors show that either coarse‑graining the dynamics or coupling to an external heat bath can induce exactness, leading entropy to evolve toward a maximum. They find that asymptotic periodicity guarantees at least one metastable equilibrium and a preparation‑dependent entropy maximum, ergodicity is both necessary and sufficient for a unique equilibrium, and exactness is required and sufficient for the global evolution of entropy to a unique maximum from any initial state.

Abstract

Thermodynamic states are assumed to be characterized by densities. Recent ergodic-theory results on the evolution of densities are used to give a unified treatment of the origin of classical nonequilibrium thermodynamic behavior. Asymptotic periodicity is sufficient for the existence of at least one state of (metastable) thermodynamic equilibrium and for the evolution of the entropy to a relative maximum that depends on the way the system is prepared. Ergodicity is necessary and sufficient for a unique state of thermodynamic equilibrium to exist. Exactness, a property of chaotic semidynamical (irreversible) systems, is necessary and sufficient for the global evolution of the entropy to its unique maximum for all initial states. Since all of the laws of physics are formulated as (reversible) dynamical systems, it is unclear why entropy is observed to approach a maximum. Setting aside the possibility that all of the laws of physics are incorrectly formulated, it is demonstrated that either observation of a subset of the complete dynamics (trivial coarse graining) or interactions with an external heat bath (addition of noise) may induce exactness with a consequent evolution of entropy to a maximal state.