Irreversible Entropy Production rate in a parametrically driven-dissipative System: The Role of Self-Correlation between Noncommuting Observables

TL;DR

This paper derives an analytical expression for the Wigner entropy production rate in a two-mode Gaussian system with parametric amplification, revealing how self-correlation and squeezing influence entropy flow and system efficiency.

Contribution

It provides a novel analytical framework linking self-correlation, squeezing, and entropy production in a driven-dissipative quantum system.

Findings

Self-correlation increases vacuum entropy production.

Squeezing reduces heat current between modes.

Squeezing constrains heat engine efficiency.

Abstract

In this paper, we explore the emergence of the Wigner entropy production rate in the stationary state of a two-mode Gaussian system. The interacting modes dissipate into different local thermal baths. Also, one of the bosonic modes evolves into the squeezed-thermal state because of the parametric amplification process. Using the Heisenberg-Langevin approach, combined with quantum phase space formulation, we get an analytical expression for the steady-state Wigner entropy production rate. It contains two key terms. The first one is an Onsager-like expression that describes heat flow within the system. The second term resulted from vacuum fluctuations of the baths. Analyses show that self-correlation between the quadratures of the parametrically amplified mode pushes the mode towards the thermal squeezed state. It increases vacuum entropy production of the total system and reduces the heat current between the modes. The results imply that, unlike other previous proposals, squeezing can constrain the efficiency of actual non-equilibrium heat engines by irreversible flows.