On the Relation Between the Second Law of Thermodynamics and Classical and Quantum Mechanics

Abstract

This article is devoted to the relation between the second law of thermodynamics, which applies to closed macroscopic systems consisting of an extremely large number of particles, such as liquids or gases, and classical or quantum mechanics, which are theories that describe systems of interacting particles on a microscopic level.In textbooks on statistical mechanics, on 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 will 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 will 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.