Alberto Frigerio

Markov dilations and quantum detailed balance

We construct quantum stochastic processes whose multi-time correlation functions, with suitable time ordering, can be obtained from a quantum dynamical semigroup. We prove that such a process defines a stationary Markov dilation of the associated semigroup if and only if (up to technicalities) the semigroup satisfies the quantum detailed balance condition with respect to its stationary state.

The zeroth law of thermodynamics

We discuss a convenient formulation of the most intuitive property of equilibrium, the zeroth law of thermodynamics, in terms of conditions of dynamical stability for a system which may interact (weakly) with its surroundings. This allows us to provide a completely rigorous, though elementary, justification of the Gibbs canonical ensemble as the description of thermodynamical equilibrium for a spatially confined quantum system with a fixed, finite number of particles. For quantum systems with variable particle numbers, the same kind of assumptions leads to the grand-canonical ensemble.