Abstract
The time evolution of an open system of infinitely many two-dimensional classical particles is investigated. Particles are interacting by a singular pair potentialU, and each particle is connected to a heat bath of temperatureT. The heat baths are represented by independent white noise forces and Langevin damping terms. Existence of strong solutions to the corresponding infinite system of stochastic differential equations is proved for initial configurations with a logarithmic order of energy fluctuations. Gibbs states forU at temperatureT are invariant under time evolution.
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References
O. E. Lanford III, The classical mechanics of one-dimensional systems of infinitely many particles, I. An existence theorem,Commun. Math. Phys. 9:169 (1968); II. Kinetic theory,Commun. Math. Phys. 11:257 (1969).
O. E. Lanford III, Time evolution of large classical systems, inDynamical Systems, Theory and Applications (Lecture Notes in Phys, Vol. 38, Springer, Berlin, 1975), pp. 1–111.
R. L. Dobrushin and J. Fritz, Non-equilibrium dynamics of one-dimensional infinite particle systems with a hard-core interaction,Commun. Math. Phys. 55:275 (1977).
J. Fritz and R. L. Dobrushin, Non-equilibrium dynamics of two-dimensional infinite particle systems with a singular interaction,Commun. Math. Phys. 57:67 (1977).
R. Lang, Unendlich-dimensionale Wienerprozesse mit Wechselwirkung. I. Existenz,Z. Wahrscheinlichkeitstheorie Verw. Gebiete 38:55 (1977); II. Die reversible Masse sind kanonische Gibbs-Masse,Z. Wahrscheinlichkeitstheorie Verw. Gebiete 39:277 (1977).
H. O. Georgii, Canonical and grand canonical Gibbs states for continuum systems,Commun. Math. Phys. 48:31 (1976).
H. P. McKean, Jr.,Stochastic Integrals (Academic Press, New York, 1969).
D. Ruelle, Superstable interactions in classical statistical mechanics,Commun. Math. Phys. 18:127 (1970).
R. L. Dobrushin, Gibbsian random fields. I, II, III,Punkts. Anal. Pril. 2:31,3:27 (1969).
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Fritz, J. Stochastic dynamics of two-dimensional infinite-particle systems. J Stat Phys 20, 351–369 (1979). https://doi.org/10.1007/BF01011777
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DOI: https://doi.org/10.1007/BF01011777