Stationary states for a mechanical system with stochastic boundary conditions
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We consider a system of Newtonian particles, with a long-range repulsive pair potential, moving in a cavity whose surface temperature is spatially varying. When a particle hits the surface, it is “thermalized” at the temperature of the collision point. We prove that this system has a unique stationary ensemble, to which any initial distribution converges for large times. We show that this stationary ensemble depends continuously on the surface temperature profile.
Key wordsNonequilibrium steady state Newtonian Markov process stationary probability measure heat flow
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