Thermodynamic Formalism: Non-additive Aspects and Related Topics

Thermodynamic formalism provides a mathematical framework for studying qualitative and quantitative aspects of dynamical systems. Founders of this theory include Sinai, Bowen, and Ruelle, but principle ideas have their origin in the development by Gibbs to describe interacting particle physical systems in the realm of statistical mechanics. Key concepts include Bernoulli and Gibbs distributions, equilibrium states, variational and, in particular, maximum entropy principles. Its contemporary mathematical aspects are intimately related with ergodic theory and have applications in fractal geometry, the description of large deviations, multifractal analysis, analysis of axiom A-systems, rigidity problems, ergodic optimization and control problems, among many others. There are also relations to geometry and group theory.