Method for Describing Non-Markovian Processes Defined by a System of Linear Integral Equations

Authors: Morozov A.N. Published: 27.09.2017
Published in issue: #5(74)/2017  
DOI: 10.18698/1812-3368-2017-5-57-66

Category: Physics | Chapter: Theoretical Physics  
Keywords: brownian motion, characteristic  function, non-markovian process, non-equilibrium state, entropy generation, flicker noise

We suggest a method for determining characteristic functions of a non-markovian stochastic process when a system of linear integral equations describes it. We show that in this case it is possible to find the solution to this problem using a previously developed method for determining characteristic functions of a process described by a single linear integral equation. We employed the method we developed to describe Brownian motion in equilibrium and non-equilibrium media. We computed spectral density of impulse fluctuations for a Brownian particle in a non-equilibrium medium and determined that in the low-frequency region it is represented by flicker noise. We show that the spectral density of impulse fluctuations for a Brownian particle in a non-equilibrium medium is a linear function of entropy generation


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