Thermodynamic Entropy as a Noether Invariant from Contact Geometry

Abstract

We use a formulation of Noether’s theorem for contact Hamiltonian systems to derive a relation between the thermodynamic entropy and the Noether invariant associated with time-translational symmetry. In the particular case of thermostatted systems at equilibrium, we show that the total entropy of the system plus the reservoir are conserved as a consequence thereof. Our results contribute to understanding thermodynamic entropy from a geometric point of view.

Keywords

• Noether’s theorem
• Hamiltonian systems
• contact geometry
• entropy
• thermostatted systems