Abstract
The physics of driven-dissipative transitions is currently a topic of great interest, particularly in quantum optical systems. These transitions occur in systems kept out of equilibrium and are therefore characterized by a finite entropy production rate. However, very little is known about how the entropy production behaves around criticality and all of it is restricted to classical systems. Using quantum phase-space methods, we put forth a framework that allows for the complete characterization of the entropy production in driven-dissipative transitions. Our framework is tailored specifically to describe photon loss dissipation, which is effectively a zero temperature process for which the standard theory of entropy production breaks down. As an application, we study the open Dicke and Kerr models, which present continuous and discontinuous transitions, respectively.We find that the entropy production naturally splits into two contributions. One matches the behavior observed in classical systems. The other diverges at the critical point.
Highlights
The entropy of an open system is not conserved in time, but instead evolves according to dS(t ) = (t ) − (t ), (1)dt where 0 is the irreversible entropy production rate and is the entropy flow rate from the system to the environment
This paper provides a framework for computing the entropy production for the zero-temperature dissipation appearing in driven-dissipative models
We applied our formalism to two widely used models. In both cases we found that one contribution u behaved qualitatively similar to that of the entropy production in classical dissipative transitions
Summary
All these results indicate that the entropy production is finite across a dissipative transition, presenting either a kink or a discontinuity This general behavior was recently shown by some of us to be universal for systems described by classical Pauli master equations and breaking a Z2 symmetry [51]. The problem is that photon losses are modeled effectively as a zero-temperature bath, for which the standard theory of entropy production yields unphysical results (it is infinite regardless of the state or the process) [55,56] This “zero-temperature catastrophe” [57,58] occurs because the theory relies on the existence of fluctuations which, in classical systems, seize completely as T → 0. The dissipative part, on other hand, is proportional to the variance of the order parameter and diverges at the critical point
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