Abstract
These are the lecture notes for the course given at the “XXVII International Fall Workshop on Geometry and Physics” held in Seville (Spain) in September 2018. We review the geometric formulation of equilibrium thermodynamics by means of contact geometry, together with the associated metric structures arising from thermodynamic fluctuation theory and the use of Hamiltonian flows to describe thermodynamic processes. Finally, we discuss the state of the art of the subject, its connection with other areas of physics, and suggest several possible further directions.
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