Abstract
A chain of one-dimensional oscillators is considered. They are mechanically uncoupled and interact via a stochastic process which redistributes the energy between nearest neighbors. The total energy is kept constant except for the interactions of the extremal oscillators with reservoirs at different temperatures. The stationary measures are obtained when the chain is finite; the thermodynamic limit is then considered, approach to the Gibbs distribution is proven, and a linear temperature profile is obtained.
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Z. Rieder, J. L. Lebowitz, and E. Lieb,J. Math. Phys. 8:1073 (1967); H. Spohn and J. L. Lebowitz,Commun. Math. Phys. 54:97 (1977).
M. Bolsterli, M. Rieh, and W. M. Visscher, Simulation of non-harmonic interactions in a crystal by self-consistent reservoirs,Phys. Rev. A 1:1086–1088 (1970); M. Rich and W. M. Visscher, Disordered harmonic chain with self consistent reservoirs,Phys. Rev. B 11:2164–2170 (1975).
A. Galves, C. Kipnis, C. Marchioro, and E. Presutti, Non equilibrium measures which exhibit a temperature gradient: study of a model,Commun. Math. Phys. 81:127–147 (1981).
V. B. Minassian, Some results concerning local equilibrium Gibbs distributions,Sov. Math. Dokl. 19:1238–1242 (1978).
T. M. Liggett, The stochastic evolution of infinite systems of interacting particles,Lecture Notes in Mathematics, No. 598, pp. 188–248 (Springer, Berlin, 1976).
E. B. Davies, A model of heat conduction,J. Stat. Phys. 18:161–170 (1978).
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Kipnis, C., Marchioro, C. & Presutti, E. Heat flow in an exactly solvable model. J Stat Phys 27, 65–74 (1982). https://doi.org/10.1007/BF01011740
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DOI: https://doi.org/10.1007/BF01011740