Stability, detailed balance and KMS condition for quantum systems.

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.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.

arXiv:quant-ph/0209088International Journal of Modern Physics BFeb 20, 200423 citations

Weighted detailed balance and local KMS condition for non-equilibrium stationary states

Luigi Accardi, Franco Fagnola, Roberto B. Quezada

We give a general definition of the local KMS condition and we prove its equivalence with a nonlinear Gibbs prescription. We discuss the irreversible $(H, \beta)$ -KMS condition, its connections with the local KMS condition and we study the irreversible $(H, \beta)$ -KMS condition for Markov generators of stochastic limit type. We introduce a definition of weighted detailed balance based on the notion of current decomposition and discuss invariant states with constant micro--currents. As an example, we construct a non-equilibrium steady state for a quantum spin chain coupled to two reservoirs at different temperatures and study its cycle dynamics and entropy production.We give a general definition of the local KMS condition and we prove its equivalence with a nonlinear Gibbs prescription. We discuss the irreversible $(H, \beta)$-KMS condition, its connections with the local KMS condition and we study the irreversible $(H, \beta)$-KMS condition for Markov generators of stochastic limit type. We introduce a definition of weighted detailed balance based on the notion of current decomposition and discuss invariant states with constant micro--currents. As an example, we construct a non-equilibrium steady state for a quantum spin chain coupled to two reservoirs at different temperatures and study its cycle dynamics and entropy production.

Jan 1, 20118 citations

We give a general definition of the local KMS condition and we prove its equivalence with a nonlinear Gibbs prescription. We discuss the irreversible

(H, \beta)

-KMS condition, its connections with the local KMS condition and we study the irreversible

(H, \beta)

-KMS condition for Markov generators of stochastic limit type. We introduce a definition of weighted detailed balance based on the notion of current decomposition and discuss invariant states with constant micro--currents. As an example, we construct a non-equilibrium steady state for a quantum spin chain coupled to two reservoirs at different temperatures and study its cycle dynamics and entropy production.