Dissipation and the Relaxation to Equilibrium

Abstract

Using the recently derived Dissipation Theorem and a corollary of the Transient Fluctuation Theorem (TFT), namely the Second Law Inequality, we derive the unique time independent, equilibrium phase space distribution function for an ergodic Hamiltonian system in contact with a remote heat bath. We prove under very general conditions that any deviation from this equilibrium distribution breaks the time independence of the distribution. Provided temporal correlations decay, and the system is ergodic, we show that any nonequilibrium distribution that is an even function of the momenta, eventually relaxes (not necessarily monotonically) to the equilibrium distribution. Finally we prove that the negative logarithm of the microscopic partition function is equal to the thermodynamic Helmholtz free energy divided by the thermodynamic temperature and Boltzmann's constant. Our results complement and extend the findings of modern ergodic theory and show the importance of dissipation in the process of relaxation towards equilibrium.

18 pages, no figures

References in corpus (4)

• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Fluctuation Theorems
• Fluctuations in Nonequilibrium Statistical Mechanics: Models, Mathematical Theory, Physical Mechanisms
• Statistical Mechanics of Time Independent Non-Dissipative Nonequilibrium States

Cited by in corpus (7)

• Monotone return to steady nonequilibrium
• On the relaxation to nonequilibrium steady states
• Equilibration and Thermalization of Classical Systems
• Quasiclassical approaches to the generalized quantum master equation
• Strong slowing down of the thermalization process of solids interacting in extreme near-field regime
• Equilibrium Stochastic Delay Processes
• Equilibrium free energy differences at different temperatures from a single set of nonequilibrium transitions