Continuous time thermodynamic formalism: for the Skorokhod space and for quantum Markov semigroups

Abstract

This thesis consists of two different works with a similar motivation. The common ground for them is the theory of Thermodynamic Formalism, (see, for instance, [LMMS15]). In the classical setting, one seeks the thermodynamical equilibrium states of a system under the action of a potential. This is done by looking for variational principles, where entropy and the Ruelle operator play central roles. An important issue is to introduce an a priori probability for defining the Ruelle operator. The two works are extensions of this theory to adjacent subjects.