On the detailed balance condition for non-hamiltonian systems

A. Frigerio, V. Gorini, Maurizio Verri

S.S. Sannikov, I. I. Uvarov

Franco Fagnola, Veronica Umanità

The classical detailed balance, or reversibility, condition admits several non-commutative extensions. We discuss the most appropriate in view of our previous results and the complete case study of three-level systems.

Luigi Accardi, Kentaro Imafuku

The principle of detailed balance is at the basis of equilibrium physics and is equivalent to the Kubo–Martin–Schwinger (KMS) condition (under quite general assumptions). In the present paper we prove that a large class of non-equilibrium quantum systems satisfies a dynamical generalization of the detailed balance condition (dynamical detailed balance) expressing the fact that all the micro-currents, associated to the Bohr frequencies are constant. The usual (equilibrium) detailed balance condition is characterized by the property that this constant is identically zero. From this we deduce a simple and experimentally measurable relation expressing the microcurrent associated to a transition between two levels ∊m→∊n as a linear combination of the occupation probabilities of the two levels, with coefficients given by the generalized susceptivities (transport coefficients). We then give a second characterization of the dynamical detailed balance condition using a master equation rather than the microcurrents. Finally we show that these two conditions are equivalent to a "local" generalization of the usual KMS condition. Summing up: rather than postulating some ansatz on the basis of phenomenological models or of numerical simulations, we deduce, directly in the quantum domain and from fundamental principles, some natural and simple non equilibrium generalizations of the three main characterizations of equilibrium states. Then we prove that these three, apparently very far, conditions are equivalent. These facts support our convinction that these three equivalent conditions capture a universal aspect of non equilibrium phenomena.

Rodanthy Tzani

Kuan-Meng Zhang, Yi-Xin Chen

In quantum information and quantum computation, a bipartite system provides a basic few-body framework for investigating significant properties of thermodynamics and statistical mechanics. A Hamiltonian model for a bipartite system is introduced to analyze the important role of interaction between bipartite subsystems in quantum non-equilibrium thermodynamics. We illustrate discrimination between such quantum thermodynamics and classical few-body non-equilibrium thermodynamics. By proposing a detailed balance condition of the bipartite system, we generally investigate the properties of the entropy and heat of our model, as well as the relation between them.