Entropy Production in Non-Linear, Thermally Driven Hamiltonian Systems

Abstract

We consider a finite chain of non-linear oscillators coupled at its ends to two infinite heat baths which are at different temperatures. Using our earlier results about the existence of a stationary state, we show rigorously that for arbitrary temperature differences and arbitrary couplings, such a system has a unique stationary state. (This extends our earlier results for small temperature differences.) In all these cases, any initial state will converge (at an unknown rate) to the stationary state. We show that this stationary state continually produces entropy. The rate of entropy production is strictly negative when the temperatures are unequal and is proportional to the mean energy flux through the system.

References in corpus (4)

• Fluctuation theorem for stochastic dynamics
• Non-Equilibrium Statistical Mechanics of Anharmonic Chains Coupled to Two Heat Baths at Different Temperatures
• Stationary Nonequilibrium States in Boundary Driven Hamiltonian Systems: Shear Flow
• Chaotic Hypothesis and Universal Large Deviations Properties

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