Continuous time thermodynamic formalism: for the Skorokhod space and for quantum Markov semigroups
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Date
2022Author
Advisor
Co-advisor
Academic level
Doctorate
Type
Subject
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 t ...
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. ...
Institution
Universidade Federal do Rio Grande do Sul. Instituto de Matemática e Estatística. Programa de Pós-Graduação em Matemática.
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