Dynamics of states of infinite quantum systems as a cornerstone of the second law of thermodynamics

TL;DR

This paper refines the second law of thermodynamics for quantum spin systems, demonstrating that entropy increases in adiabatically closed systems, with examples illustrating pure to mixed state transitions in specific models.

Contribution

It advances the deterministic formulation of the second law for quantum systems, including new insights into entropy dynamics in models exhibiting quantum chaos.

Findings

Entropy increases to a maximum in adiabatically closed quantum systems.

Transition from pure to mixed states observed in exponential and Dyson models.

Evidence of quantum chaos in the Dyson model dynamics.

Abstract

We improve on our version of the second law of thermodynamics as a deterministic theorem for quantum spin systems in two basic aspects. The first concerns the general statement of the second law: spontaneous changes in an adiabatically closed system will always be in the direction of increasing mean entropy, which rises to a maximal value. Two specific examples concern the transition from pure to mixed states in two different universality classes of dynamics in one dimension, one being the exponential model, the other the Dyson model, the dynamics of the latter exhibiting strong graphical evidence of quantum chaos, as a consequence of the results of Albert and Kiessling on the Cloitre function.