Stationary states for a mechanical system with stochastic boundary conditions
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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- 1.S. Goldstein, J. L. Lebowitz, and E. Presutti, Mechanical systems with stochastic boundaries, inRandom Fields, J. Fritz, J. L. Lebowitz, and D. Szasz, eds. (North-Holland, Amsterdam, 1981).Google Scholar
- 2.S. Goldstein, J. L. Lebowitz, and K. Ravishankar,Commun Math. Phys. 85:419 (1982).Google Scholar
- 3.J. Farmer, S. Goldstein, and E. R. Speer,J. Stat. Phys. 34:263 (1984).Google Scholar
- 4.C. Marchioro, A. Pellegrinotti, E. Presutti, and M. Pulvirenti,J. Math. Phys. 17(5):647 (1976).Google Scholar
- 5.J. T. Schwartz,Differential Geometry and Topology (Gordon and Breach, New York, 1968); J. Milnor,Topology from the differential viewpoint (The University Press of Virginia, Charlottesville, 1965).Google Scholar
- 6.S. Goldstein, J. L. Lebowitz, K. Ravishankar, Approach to equilibrium in models of a system in contact with a heat bath (unpublished).Google Scholar
- 7.J. L. Lebowitz and P. G. Bergmann,Ann. Phys. (N.Y.) 1:1 (1957).Google Scholar
- 8.J. L. Lebowitz and H. Spohn,J. Stat. Phys. 19:633 (1978).Google Scholar
- 9.C. Bardos, R. Caflisch, and B. Nicolaenko, Thermal layer solutions of the Boltzmann equation, inStatistical Physics and Dynamical Systems, J. Fritz, A. Jaffe, and D. Szasz, eds. (Birkhäuser, Boston, 1985).Google Scholar
- 10.N. Ianiro and J. L. Lebowitz,Found. Phys. 15:531 (1985).Google Scholar