Thermodynamic Entropy as a Noether Invariant from Contact Geometry
Alessandro Bravetti, Miguel Ángel García-Ariza, Diego Tapias
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.
Topics & Concepts
Noether's theoremEntropy (arrow of time)Invariant (physics)MathematicsMaximum entropy thermodynamicsEntropy in thermodynamics and information theoryMathematical physicsPhysicsJoint quantum entropyClassical mechanicsStatistical physicsThermodynamicsLagrangianPrinciple of maximum entropyStatisticsAdvanced Thermodynamics and Statistical MechanicsControl and Stability of Dynamical SystemsThermoelastic and Magnetoelastic Phenomena