H-theorem in quantum physics

TL;DR

This paper connects quantum information theory with physical observables to formulate a quantum H-theorem, exploring the second law of thermodynamics in quantum systems and identifying conditions for its violation.

Contribution

It introduces a formulation of the quantum H-theorem based on physical observables, linking quantum information results to real quantum system evolution.

Findings

Quantum H-theorem expressed in terms of physical observables.

Identification of conditions where the second law can be violated.

Typical energy-isolated quantum systems evolve with non-diminishing entropy.

Abstract

Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.