Abstract
The relaxation properties of a small classical system weakly coupled to a large classical system which acts as a heat bath are described using a generalized Fokker-Planck equation. The Fokker-Planck equation is derived in general using a modification of the elimination of fast variables techniques previously described. The specific example in which the small system is a harmonic oscillator linearly coupled to the heat bath is treated in detail and it is demonstrated that there is a dynamic frequency shift as well as a statistical shift of the oscillator frequency.
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Romero-Rochin, V., Oppenheim, I. Relaxation properties of weakly coupled classical systems. J Stat Phys 53, 307–322 (1988). https://doi.org/10.1007/BF01011559
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DOI: https://doi.org/10.1007/BF01011559