Entropy production and nonequilibrium stationarity in quantum dynamical systems

Tatsuro Yuge, Takahiro Sagawa, Ayumu Sugita +1 more

Ricardo Gutiérrez, Juan P. Garrahan, Igor Lesanovsky

Dense Rydberg gases are out-of-equilibrium systems where strong density-density interactions give rise to effective kinetic constraints. They cause dynamic arrest associated with highly constrained many-body configurations, leading to slow relaxation and glassy behavior. Multicomponent Rydberg gases feature additional long-range interactions such as excitation exchange. These are analogous to particle swaps used to artificially accelerate relaxation in simulations of atomistic models of classical glass formers. In Rydberg gases, however, swaps are real physical processes, which provide dynamical shortcuts to relaxation. They permit the accelerated approach to stationarity in experiment and at the same time have an impact on the nonequilibrium stationary state. In particular, their interplay with radiative decay processes amplifies irreversibility of the dynamics, an effect which we quantify via the entropy production at stationarity. Our work highlights an intriguing analogy between real dynamical processes in Rydberg gases and artificial dynamics underlying advanced Monte Carlo methods. Moreover, it delivers a quantitative characterization of the dramatic effect swaps have on the structure and dynamics of their stationary state.

Irene Ada Picatoste, Alessandra Colla, Heinz-Peter Breuer

We discuss fundamental features of the local expression for the entropy production rate of the nonequilibrium quantum dynamics of open systems and its relations to memory effects and the spectrum of the generator of the dynamics. Defining the entropy production rate as negative rate of change of the relative entropy with respect to an instantaneous fixed point, it is shown that positivity of the entropy production rate for all possible initial states implies that the real parts of the eigenvalues of the time-local generator for the quantum master equation are always negative. It is further demonstrated that Markovian dynamics, identified as P-divisibility of the quantum dynamical map, implies positivity of entropy production rate, thus providing a kind of generalized second law in the nonequilibrium regime. We also prove by means of the counterexample of a phase covariant quantum master equation that the converse of this statement is not true, i.e., there are non-Markovian dynamics for which the entropy production rate is always positive. Thus, we conclude that the emergence of negative entropy production rates is a sufficient but not necessary condition for non-Markovianity of the quantum dynamics. Finally, we also consider a recently introduced map-based notion of entropy production and show the equivalence between its positivity and Markovianity for general finite-dimensional systems.

K. Lendi

Göran Lindblad

A. Tejero

The asymmetry between heating and cooling in open quantum systems is a hallmark of nonequilibrium dynamics, yet its thermodynamic origin has remained unclear. Here, we investigate the thermalization of a quantum system weakly coupled to a thermal bath, focusing on the entropy production rate and the quantum thermokinetic uncertainty relation (TKUR). We derive an analytical expression for the entropy production rate, showing that heating begins with a higher entropy production, which drives faster thermalization than cooling. The quantum TKUR links this asymmetry to heat-current fluctuations, demonstrating that larger entropy production suppresses fluctuations, making heating more stable than cooling. Our results reveal the thermodynamic basis of asymmetric thermalization and highlight uncertainty relations as key to nonequilibrium quantum dynamics.