Quantum dynamical semigroups and approach to equilibrium

Herbert E. Spohn

Robert Alicki, K. Lendi

Fabricio Toscano, F. Nicacio

We characterize all Gaussian dynamical semigroups in continuous-variables quantum systems of $n$-bosonic modes which have a thermal Gibbs state as a stationary solution. This is performed through an explicit relation between the diffusion and dissipation matrices, which characterize the semigroup dynamics, and the covariance matrix of the thermal equilibrium state. We also show that Alicki's quantum detailed-balance condition, based on a Gelfand-Naimark-Segal inner product, allows the determination of the temperature dependence of the diffusion and dissipation matrices and the identification of different Gaussian dynamical semigroups which share the same thermal equilibrium state.

Herbert E. Spohn

In analogy to the phenomenological theory of irreversible thermodynamics we define the entropy production for an arbitrary quantum dynamical semigroup with a stationary state. We prove that the entropy production is convex and positive and that the entropy production is a measure of dissipativity of the semigroup. The entropy production is used to prove the approach to equilibrium and to classify the stationary states of semigroups arising in the weak coupling limit.

Dharmendra Kumar, Kalyan B. Sinha, Sachi Srivastava

Wawrzyniec Guz