Wehrl entropy production theory for non-equilibrium quantum systems

Zeyu Liu, Yun‐Jie Xia, Zhong‐Xiao Man

Bruno O. Goes

The physics of systems out of equilibrium is a topic of great interest, mainly due to the possibility of exploring phenomena that can not be observed in equilibrium systems. Driven-dissipative phase transitions open the opportunity of studying phases with no classical counterparts, and these can be experimentally realized in quantum optical platforms. Since these transitions occur in systems kept out of equilibrium, they are characterized by a finite entropy production rate. However, due to technical difficulties regarding the zero temperature limit and the non-gaussianity of such models, very little is known about how entropy production behaves around criticality. Using a quantum phase-space method, based on the Husimi Q-function, we put forth a framework that allows for the complete characterization of the entropy production in driven-dissipative transitions. This new theoretical 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. It makes no assumptions about Gaussianity about the model or the state. It works for both, steady-states as well as the dynamics and as an application, we study both situations in the paradigmatic driven-dissipative Kerr model, which presents a discontinuous phase transition. For general driven-dissipative critical systems, where one can define a thermodynamic limit, we find that the entropy production rate and flux naturally split into two contributions: an extensive one and a contribution due to quantum fluctuations only. Moreover, we identify a contribution to the entropy production due to unitary dynamics, and we find that the behavior of this contribution at the non-equilibrium steady-state (NESS) matches the behavior of entropy production rate observed in classical systems. The quantum contributions are found to diverge at the critical point.

Y. Tokura

Hidekazu Tsukiji, Teiji Kunihiro, Akira Ohnishi A +1 more

We investigate the thermalization process from a glasma-like initial condition in a static box in terms of the Husimi–Wehrl (HW) entropy defined with the Husimi function, a quantum distribution function in a phase space. We calculate the semiclassical time evolution of the HW entropy in Yang–Mills field theory with the phenomenological initial field configuration given by mimicking the McLerran–Venugopalan model in a static box, which has instability triggered by initial field fluctuations. Husimi–Wehrl entropy production implies the thermalization of the system and it reflects the underlying dynamics such as chaoticity and instability. By comparing the production rate with the Kolmogorov–Sinaï rate, we find that the HW entropy production rate is significantly larger than that expected from chaoticity. We also show that the HW entropy is finally saturated when the system reaches a quasi-stationary state. The saturation time of the HW entropy is comparable with that of pressure isotropization, which is around 1 fm/c in the present calculation.

Izumi Ojima

Hidekazu Tsukiji, Teiji Kunihiro, Akira Ohnishi +1 more

We investigate the thermalization process from a glasma-like initial condition in a static box in terms of the Husimi–Wehrl (HW) entropy defined with the Husimi function, a quantum distribution function in a phase space. We calculate the semiclassical time evolution of the HW entropy in Yang–Mills field theory with the phenomenological initial field configuration given by mimicking the McLerran–Venugopalan model in a static box, which has instability triggered by initial field fluctuations. Husimi–Wehrl entropy production implies the thermalization of the system and it reflects the underlying dynamics such as chaoticity and instability. By comparing the production rate with the Kolmogorov–Sinaï rate, we find that the HW entropy production rate is significantly larger than that expected from chaoticity. We also show that the HW entropy is finally saturated when the system reaches a quasi-stationary state. The saturation time of the HW entropy is comparable with that of pressure isotropization, which is around 1 fm/|$c$| in the present calculation.