Approach to Thermodynamic Equilibrium (and other Stationary States)

Willis E. Lamb

A. M. Perelomov

Maurizio Fagotti

Equilibrium thermodynamics emerges because a vast number of microscopic states become indistinguishable at the level of local observables. We start from the observation that a nonequilibrium quantum state can also be represented by an ensemble of pure states that minimizes the average energy variance. We show that varying the statistical weights within this optimal family organizes state space into ``minimum-variance leaves'', which generalize the space of stationary states underlying equilibrium. We observe thermodynamic compression on the leaves, which in the simplest scenario manifests itself in the indistinguishability of states with the same energy density. We call this ``leaf typicality''; at equilibrium it reduces to eigenstate thermalization or its generalizations. Numerical tests support leaf typicality on some leaves and indicate a breakdown of its stronger forms on others, suggesting a rich thermodynamic organization beyond equilibrium. These results open a route to a unified statistical mechanics of equilibrium and nonequilibrium quantum states.

V. S. Babichenko

Properties of low energy spectrum of elementary excitations in nonequilibrium Bose gas in stationary state with the dynamical equilibrium of outgoing and incoming of particles are studied. It is shown that due to the noise effect, typical for nonequilibrium systems, this spectrum has a diffusion character, in contradiction with the thermodynamically equilibrium systems, where this spectrum has a sound form.

Walter Greiner, Ludwig Neise, Horst Stöcker B

Pablo Carlos López Vázquez, Andrés García, Gilberto Sánchez‐González

Abstract We describe the features of the non-equilibrium stationary states reached by a kicked linear chain made of three qubits in contact with a zero temperature dissipative environment and report the emergence of stationary entanglement between a pair of qubits of the linear chain when periodic kicks are applied simultaneously to this pair of qubits. In our scheme, the steady entanglement emerges as a result of the collective action of dissipation and kicks. We explore in this paper some of the conditions under which stationary entanglement emerges. Furthermore, the application of periodic kicks as the driven mechanism, allows us to calculate in a simple way, some of the thermodynamical properties of the non-equilibrium steady states and study their relation to the emergence of entanglement.