Irreversible entropy production rate in a parametrically driven-dissipative system: The role of self-correlation between noncommuting observables

In this paper, we explore 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 HeisenbergLangevin approach combined with the 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 results from vacuum fluctuations of the baths. Analyses show that self-correlation between the quadratures of the parametrically amplified mode pushes the mode toward 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 in previous proposals, squeezing can constrain the efficiency of actual nonequilibrium heat engines by irreversible flows.