Organizer: Prof. Dr. Gernot Albe
One of the basic postulates of statistical physics states that an equilibrium state of a macroscopic system is characterized by the maximum of its entropy under given constrains (usually integral of motions). The description of such states requires only a small number of parameters and these states take the form of a generalized Gibbs state. Recently it has been found generalized Gibbs states play an important role in description of equilibrium quantum states also on smaller scales.
However, why the maximum entropy principle, and consequently the use of the Gibbs form, could be the proper paradigm for constructing the quantum equilibrium state has been the subject of much debate and it remains rather unclear. Here we study generalized Gibbs states in the context of quantum Markov processes (including both discrete and continues). For a broad class of quantum Markov processes we identify their asymptotic states as well as their integral of motions. Based on their algebraic properties and mutual relationships we reveal that all their resulting equilibrium states can be casted in a Gibbs-like form.