Thermodynamics of linear open quantum walks

TL;DR

This paper explores the thermodynamics of linear open quantum walks, defining equilibrium properties, analyzing thermalization, and examining the validity of thermodynamic laws in a quantum environment-driven system.

Contribution

It introduces a comprehensive thermodynamic framework for linear open quantum walks, including equilibrium, nonequilibrium, and dissipative quantum computation aspects.

Findings

Identified an equilibrium temperature and population inversion.

Analyzed the thermalization process and entropy evolution.

Validated the second and third laws of thermodynamics in this quantum setting.

Abstract

Open quantum systems interact with their environment, leading to nonunitary dynamics. We investigate the thermodynamics of linear Open Quantum Walks (OQWs), a class of quantum walks whose dynamics is entirely driven by the environment. We define an equilibrium temperature, identify a population inversion near a finite critical value of a control parameter, analyze the thermalization process, and develop the statistical mechanics needed to describe the thermodynamical properties of linear OQWs. We also study nonequilibrium thermodynamics by analyzing the time evolution of entropy, energy, and temperature, while providing analytical tools to understand the system's evolution as it converges to the thermalized state. We examine the validity of the second and third laws of thermodynamics in this setting. Finally, we employ these developments to shed light on dissipative quantum computation within the OQW framework.