Title: Generalized Fokker-Planck equation and its solution for linear non-Markovian Gaussian systems
Author(s):

O.Yu. Sliusarenko (Akhiezer Institute for Theoretical Physics NSC KIPT, 1 Akademichna Str., 61108 Kharkiv, Ukraine )

In this paper we suggest a consistent approach to derivation of generalized Fokker-Planck equation (GFPE) for Gaussian non-Markovian processes with stationary increments. This approach allows us to construct the probability density function (PDF) without a need to solve the GFPE. We employ our method to obtain the GFPE and PDFs for free generalized Brownian motion and the one in harmonic potential for the case of power-law correlation function of the noise. We prove the fact that the considered systems may be described with Einstein-Smoluchowski equation at high viscosity levels and long times. We also compare the results with those obtained by other authors. At last, we calculate PDF of thermodynamical work in the stochastic system which consists of a particle embedded in a harmonic potential moving with constant velocity, and check the work fluctuation theorem for such a system.

Key words: Fokker-Planck equation, Gaussian system, non-Markovian system, thermodynamical work, transient fluctuation relation
PACS: 05.10.Gg, 52.65.Ff, 02.50.Ey, 05.40.-a

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