The second law of thermodynamics as a deterministic theorem for quantum spin systems

TL;DR

This paper discusses the second law of thermodynamics as a theorem for quantum spin systems, showing that mean entropy generally increases or remains conserved under certain transformations, with implications for quantum thermodynamics.

Contribution

It establishes that the mean entropy of quantum spin systems either grows or remains conserved during automorphic transformations, extending classical thermodynamic principles to quantum lattice systems.

Findings

Mean entropy increases under automorphic transformations.

Non-automorphic environmental interactions conserve average entropy.

Key properties like upper semicontinuity and affinity are crucial for results.

Abstract

We review our approach to the second law of thermodynamics, viewed as a theorem asserting the growth of the mean (Gibbs-von Neumann) entropy of quantum spin systems undergoing automorphic (unitary) adiabatic transformations. Non-automorphic interactions with the environment, although known to produce on the average a strict reduction of the entropy of systems with finite number of degrees of freedom, are proved to conserve the mean entropy on the average. The results depend crucially on two properties of the mean entropy, proved by Robinson and Ruelle for classical systems, and Lanford and Robinson for quantum lattice systems: upper semicontinuity and affinity.