Thermal density functional theory approach to quantum thermodynamics

TL;DR

This paper introduces a density functional theory approach to analyze quantum thermodynamics, enabling the extraction of work statistics and entropy from many-body quantum systems at finite temperature, with applications to the Hubbard model.

Contribution

It presents a novel density functional theory framework for quantum thermodynamics, linking thermodynamic quantities to densities in many-body quantum systems at finite temperature.

Findings

The method expresses work and entropy as functionals of densities.

Application to the Hubbard model reveals effects of interactions and potentials.

The approach provides insights into finite-temperature quantum processes.

Abstract

Understanding the thermodynamic properties of many-body quantum systems and their emergence from microscopic laws is a topic of great significance due to its profound fundamental implications and extensive practical applications. Recent advances in experimental techniques for controlling and preparing these systems have increased interest in this area, as they have the potential to drive the development of quantum technologies. In this study, we present a density-functional theory approach to extract detailed information about the statistics of work and the irreversible entropy associated with quantum quenches at finite temperature. Specifically, we demonstrate that these quantities can be expressed as functionals of thermal and out-of-equilibrium densities, which may serve as fundamental variables for understanding finite-temperature many-body processes. We, then, apply our method to the case of the inhomogeneous Hubbard model, showing that our density functional theory based approach can be usefully employed to unveil the distinctive roles of interaction and external potential on the thermodynamic properties of such a system.