Contact geometry for simple thermodynamical systems with friction: Contact geometry for thermodynamics

By means of the Jacobi structure associated with a contact structure, we use the so-called evolution vector field to propose a new characterization of isolated thermodynamical systems with friction, a simple but important class of thermodynamical systems which naturally satisfy the first and second laws of thermodynamics, i.e. total energy preservation of isolated systems and non-decreasing total entropy, respectively. We completely clarify its qualitative dynamics, the underlying geometrical structures and we also show how to apply discrete gradient methods to numerically integrate the evolution equations for these systems.
The authors acknowledge financial support from the Spanish Ministry of Science and Innovation, under grants PID2019-106715GB-C21, MTM2016- 76702-P, “Severo Ochoa Programme for Centres of Excellence in R&D” (SEV-2015-0554) and from the Spanish National Research Council, through the “Ayuda extraordinaria a Centros de Excelencia Severo Ochoa” (20205- CEX001). A. Simoes is supported by the FCT (Portugal) research fellowship SFRH/BD/129882/2017