Full Quantum Work Statistics for Non-Homogeneous Many-Body Systems

TL;DR

This paper develops a first-principles method within thermal density functional theory to analyze full quantum work statistics in interacting many-body systems, demonstrated on the Hubbard model, revealing phase-dependent thermodynamic responses.

Contribution

It introduces a novel approach to reconstruct relaxation functions for quantum work statistics, moving beyond phenomenological models and enabling detailed analysis of out-of-equilibrium thermodynamics in correlated systems.

Findings

Reconstructed relaxation functions from first principles.

Analyzed Mott-to-band-insulator crossover dynamics.

Provided a transferable framework for quantum thermodynamics.

Abstract

The nonequilibrium thermodynamics of interacting quantum many-body systems is investigated within the framework of thermal time-dependent density functional theory using a generalized linear-response formulation for the full quantum work statistics. A first-principles route is established to reconstruct the relaxation function that underlies linear-response theory, thereby moving beyond phenomenological descriptions and enabling a consistent evaluation of all moments of the dissipated-work distribution in interacting systems. The predictive power of the approach is demonstrated for the Hubbard model subject to a staggered external potential, where the evolution of the relaxation dynamics across the Mott-to-band-insulator crossover reveals how distinct many-body phases shape the out-of-equilibrium thermodynamic response. These results provide a microscopic and transferable framework for quantum thermodynamics in correlated systems, bridging thermal density functional theory and nonequilibrium work statistics.