The second law of Thermodynamics as a theorem in quantum mechanics

Hal Tasaki

The second law of Thermodynamics as a theorem in quantum mechanics

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arxiv cond-mat/0011321 v2 pith:5VSKUXOP submitted 2000-11-20 cond-mat.stat-mech

Hal Tasaki This is my paper · ORCID

classification cond-mat.stat-mech

keywords quantumthermodynamicstimewaitingadiabaticalmostcertainchoices

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We treat a quantum mechanical system with certain general properties which are expected to be common in macroscopic quantum systems. Starting from a PURE initial state (which may not describe an equilibrium) in which energy is mildly concentrated at a single value, we consider a time evolution determined by a time-dependent Hamiltonian as a model of an adiabatic operation in thermodynamics. We take a family of operations with the same procedure and various ``waiting times.'' Then the Minimum Work Principle is rigorously proved for almost all choices of the waiting time.

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Typical Positivity of Nonequilibrium Entropy Production for Pure States
cond-mat.stat-mech 2024-11 conditional novelty 6.0 of 10

For almost all pure states sampled from the Scrooge measure, entropy production is exponentially close to the ensemble value, so typical pure states obey the second law.

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