Journal of Statistical Physics

, Volume 164, Issue 1, pp 130–141 | Cite as

Thermostat-Like Perturbations of an Oscillator

  • Mark Freidlin


We consider an oscillator with one degree of freedom perturbed by a deterministic thermostat-like perturbation and another system, in particular, another oscillator, coupled with the first one. If the Hamiltonian of the first system has saddle points, the whole system has, in a sense, a stochastic behavior on long time intervals. Under certain conditions, one can introduce the relative entropy and describe metastability and other large deviation effects in this deterministic system. If the coupled system is also an oscillator, the long time evolution of the energy of this oscillator has a diffusion approximation. To get these results one has to regularize the system. But the results are, to some extent, independent of the regularization: the stochasticity is due to instabilities at saddle points of the original system.


Perturbations of an oscillator Large deviations Metastability 



The work was supported in part by the NSF Grant DMS 1411866.


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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA

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