On the relation between the second law of thermodynamics and classical and quantum mechanics

TL;DR

This paper critically examines the connection between the second law of thermodynamics and classical and quantum mechanics, highlighting the assumptions and limitations involved in deriving irreversibility from deterministic theories.

Contribution

It clarifies that derivations of the second law from classical mechanics involve additional assumptions and discusses the role of information and coarse-graining, contrasting classical and quantum perspectives.

Findings

Classical mechanics derivations of the second law rely on extra assumptions.

Coarse-graining reflects finite information, not ignorance.

Quantum mechanics supports entropy's finite information but doesn't explain irreversibility.

Abstract

In textbooks on statistical mechanics, one finds often arguments based on classical mechanics, phase space and ergodicity in order to justify the second law of thermodynamics. However, the basic equations of motion of classical mechanics are deterministic and reversible, while the second law of thermodynamics is irreversible and not deterministic, because it states that a system forgets its past when approaching equilibrium. I argue that all "derivations" of the second law of thermodynamics from classical mechanics include additional assumptions that are not part of classical mechanics. The same holds for Boltzmann's H-theorem. Furthermore, I argue that the coarse-graining of phase-space that is used when deriving the second law cannot be viewed as an expression of our ignorance of the details of the microscopic state of the system, but reflects the fact that the state of a system is fully specified by using only a finite number of bits, as implied by the concept of entropy, which is related to the number of different microstates that a closed system can have. While quantum mechanics, as described by the Schroedinger equation, puts this latter statement on a firm ground, it cannot explain the irreversibility and stochasticity inherent in the second law.