This work provides a theory of entropy production suitable for zero temperature baths and non-gaussian driven-dissipative models, based on the Husimi Q-function. The work focuses on driven-dissipative phase transitions where the entropy production rate and entropy flux rate split into two contributions: one extensive in the driving amplitude and the other solely due to quantum fluctuations.
This work provides a theory of entropy production suitable for zero temperature baths and non-gaussian driven-dissipative models, based on the Husimi Q-function. The work focuses on driven-dissipative phase transitions where the entropy production rate and entropy flux rate split into two contributions: one extensive in the driving amplitude and the other solely due to quantum fluctuations.
Driven-dissipative phase transitions are currently a topic of intense research due to the prospect of experimental realizations in quantum optical setups. The most paradigmatic model presenting such a transition is the Kerr model, which predicts the phenomenon of optical bistability, where the system may relax to two different steady states for the same driving condition. These states, however, are inherently out-of-equilibrium and are thus characterized by the continuous production of irreversible entropy, a key quantifier in thermodynamics. In this paper, we study the dynamics of the entropy production rate in a quench scenario of the Kerr model, where the external pump is abruptly changed. This is accomplished using a recently developed formalism, based on the Husimi Q-function, which is particularly tailored for driven-dissipative and non-Gaussian bosonic systems, Goes et al. [Phys. Rev. Res. 2, 013136 (2020)]. Within this framework, the entropy production can be split into two contributions, one being extensive with the drive and describing classical irreversibility, and the other being intensive and directly related to quantum fluctuations. The latter, in particular, is found to reveal the high degree of nonadiabaticity for quenches between different metastable states.
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.
Abstract The entropy produced when a quantum system is driven away from equilibrium can be decomposed in two parts, one related with populations and the other with quantum coherences. The latter is usually based on the so-called relative entropy of coherence, a widely used quantifier in quantum resource theories. In this paper we argue that, despite satisfying fluctuation theorems and having a clear resource-theoretic interpretation, this splitting has shortcomings. First, it predicts that at low temperatures the entropy production will always be dominated by the classical term, irrespective of the quantum nature of the process. Second, for infinitesimal quenches, the radius of convergence diverges exponentially as the temperature decreases, rendering the functions non-analytic. Motivated by this, we provide here a complementary approach, where the entropy production is split in a way such that the contributions from populations and coherences are written in terms of a thermal state of a specially dephased Hamiltonian. The physical interpretation of our proposal is discussed in detail. We also contrast the two approaches by studying work protocols in a transverse field Ising chain, and a macrospin of varying dimension.
We analyze the entropy production of Quantum Reset Models (QRMs) corresponding to quantum dynamical semigroups driven by Lindbladians motivated by a probabilistic description of dissipation in an external environment. We investigate the strict positivity of entropy production for Lindbladians given as sums of QRMs, when the Hamiltonian of the total Lindbladian is split as an affine combination of Hamiltonians of the individual QRMs. In this setup, we derive conditions on the coefficients of the combination and on the reset states ensuring either positive or zero entropy production. Second, we deal with a tri-partite system subject at its ends to two independent QRMs and a weak coupling Hamiltonian. The latter is split as an affine combination of individual Hamiltonians, and we provide necessary and sufficient conditions ensuring strict positivity of the entropy production to leading order, with the possible exception of one affine combination. We apply these results to a physically motivated model and exhibit explicit expressions for the leading orders steady-state solution, entropy production and entropy fluxes. Moreover, these approximations are numerically shown to hold beyond the expected regimes.
In thermodynamics, entropy production and work quantify irreversibility and the consumption of useful energy, respectively, when a system is driven out of equilibrium. For quantum systems, these quantities can be identified at the stochastic level by unravelling the system's evolution in terms of quantum jump trajectories. We here derive a general formula for computing the joint statistics of work and entropy production in Markovian driven quantum systems, whose instantaneous steady states are of Gibbs form. If the driven system remains close to the instantaneous Gibbs state at all times, then we show that the corresponding two-variable cumulant generating function implies a joint detailed fluctuation theorem so long as detailed balance is satisfied. As a corollary, we derive a modified fluctuation-dissipation relation (FDR) for the entropy production alone, applicable to transitions between arbitrary steady states, and for systems that violate detailed balance. This FDR contains a term arising from genuinely quantum fluctuations, and extends an analogous relation from classical thermodynamics to the quantum regime.