Aspects of the Second Law of Thermodynamics from Quantum Statistical Mechanics to Quantum Information Theory

TL;DR

This paper explores the second law of thermodynamics within quantum statistical mechanics and quantum information, using the maximum entropy principle and the Kullback-Leibler inequality to unify thermodynamic concepts and analyze entanglement effects.

Contribution

It introduces a framework combining the maximum entropy principle and master equations to generalize the second law in quantum contexts, including thermodynamics and information theory.

Findings

The second law can be formulated using quantum density matrices.

Entanglement plays a significant role in quantum thermodynamic processes.

The model illustrates entanglement's impact on Landauer's erasure principle.

Abstract

The Kullback-Leibler inequality is a way of comparing any two density matrices. A technique to set up the density matrix for a physical system is to use the maximum entropy principle, given the entropy as a functional of the density matrix, subject to known constraints. In conjunction with the master equation for the density matrix, these two ingredients allow us to formulate the second law of thermodynamics in its widest possible setting. Thus problems arising in both quantum statistical mechanics and quantum information can be handled. Aspects of thermodynamic concepts such as the Carnot cycle will be discussed. A model is examined to elucidate the role of entanglement in the Landauer erasure problem.