Entropy Dynamics in the System of Interacting Qubits

TL;DR

This paper explores how entropy behaves in interacting qubit systems, examining the effects of unital and non-unital quantum channels, and the impact of initial correlations on entropy evolution.

Contribution

It provides a detailed analysis of entropy dynamics in quantum systems, including the roles of Maxwell demons and initial correlations, extending the understanding of the quantum H-theorem.

Findings

Unital channels preserve or increase entropy, aligning with the Second Law.

Non-unital channels can decrease entropy, challenging classical thermodynamics.

Initial correlations can significantly influence entropy change in quantum evolutions.

Abstract

The classical Second Law of Thermodynamics demands that an isolated system evolves with a non-diminishing entropy. This holds as well in quantum mechanics if the evolution of the energy-isolated system can be described by a unital quantum channel. At the same time, the entropy of a system evolving via a non-unital channel can, in principle, decrease. Here, we analyze the behavior of the entropy in the context of the H-theorem. As exemplary phenomena, we discuss the action of a Maxwell demon (MD) operating a qubit and the processes of heating and cooling in a two-qubit system. We further discuss how small initial correlations between a quantum system and a reservoir affect the increase in the entropy under the evolution of the quantum system.