H-theorem and Maxwell Demon in Quantum Physics

TL;DR

This paper establishes a criterion for unital quantum channels, enabling identification of processes where entropy decreases, exemplified by quantum Maxwell demon and heating-cooling in two-qubit systems, challenging traditional thermodynamic laws.

Contribution

It introduces a general criterion for unitality in quantum evolution, facilitating the detection of entropy-decreasing processes in energy-isolated quantum systems.

Findings

Unital quantum channels preserve entropy; non-unital channels can decrease entropy.

The criterion helps identify entropy-decreasing processes like Maxwell demon.

Examples include quantum Maxwell demon and two-qubit heating-cooling process.

Abstract

The Second Law of Thermodynamics states that temporal evolution of an isolated system occurs with non-diminishing entropy. In quantum realm, this holds for energy-isolated systems the evolution of which is described by the so-called unital quantum channel. The entropy of a system evolving in a non-unital quantum channel can, in principle, decrease. We formulate a general criterion of unitality for the evolution of a quantum system, enabling a simple and rigorous approach for finding and identifying the processes accompanied by decreasing entropy in energy-isolated systems. We discuss two examples illustrating our findings, the quantum Maxwell demon and heating-cooling process within a two-qubit system.