Modeling Thermodynamic Distance, Curvature and Fluctuations

“Throughout the book, the author gathers the essential mathematical tools he uses for the presentation of the geometrization of thermodynamics. Readers who are not well acquainted with such mathematical tools will thus get in an efficient way the bases for a complete understanding of the applications of these Riemann geometric tools to thermodynamics.” (Alain Brillard, zbMATH 1361.80001, 2017)

• Introduction.- Algebraic Structures. Spaces. Reference Frames.- Calculus with Vectors and Differential Forms.- Elements of Riemann Geometry.- Equilibrium Thermodynamics.- Thermodynamics as a Contact Geometry Structure.-  Thermodynamic Distance.- Geometrization of Thermodynamic Fluctuations.- Thermodynamic Curvature. Correlation. Stability.