Brownian Motion as an Irreversible Non-Markovian Process

Authors: Morozov A.N. Published: 16.04.2019
Published in issue: #2(83)/2019  
DOI: 10.18698/1812-3368-2019-2-94-103

Category: Physics | Chapter: Theoretical Physics  
Keywords: non-Markovian process, Brownian motion, non-equilibrium state, entropy generation, flicker noise

The paper presents a method of describing Brownian motion in a non-equilibrium medium for the case of irreversible processes. We computed spectral density of velocity 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 employed the method we developed to describe Brownian motion in a non-equilibrium medium to compute fluctuations of current in a small volume of an electrolyte. We derived estimations of the Hooge parameter magnitude and the randomisation time constant for ions in an electrolyte, which match the estimations obtained via experiments


[1] Bochkov G.N., Kuzovlev Yu.E. New aspects in 1/f noise studies. Phys.-Uspekhi, 1983, vol. 26, no. 9, pp. 829–844. DOI: 10.1070/PU1983v026n09ABEH004497

[2] Kuzovlev Yu.E. Why nature needs 1/f noise. Phys.-Uspekhi, 2015, vol. 58, no. 7, pp. 719–729. DOI: 10.3367/UFNe.0185.201507d.0773

[3] Hooge F.N., Gaal J.L. Fluctuations with a 1/f spectrum in the conductance of ionic solutions and in the voltage of concentration cells. Philips Res. Rep., 1971, vol. 26, no. 2, pp. 77–90.

[4] Bezrukov S.M., Pustovoit M.A., Sibilev A.I., et al. Large-scale conductance fluctuations in solutions of strong electrolytes. Physica B: Condens. Matter, 1989, vol. 159, iss. 3, pp. 388–398. DOI: 10.1016/0921-4526(89)90016-1

[5] van den Berg R.J., de Vos A., de Goede J. Electrical noise in solutions of hydrochloric acid in ethanol. Phys. Lett. A, 1989, vol. 139, iss. 5-6, pp. 249–252. DOI: 10.1016/0375-9601(89)90149-7

[6] Hooge F.N. 1/f noise sources. IEEE Trans. Electron. Devices, 1994, vol. 41, iss. 11, pp. 1926–1935. DOI: 10.1109/16.333808

[7] Morozov A.N. On Brownian motion in medium with fluctuating transfer coefficient. Izvestiya vuzov. Fizika, 1986, no. 6, pp. 90–91 (in Russ.).

[8] Morozov A.N. Use of the theory of non-Markovian processes in the description of Brownian motion. J. Exp. Theor. Phys., 1996, vol. 82, iss. 4, pp. 703–708.

[9] Lenzi E.K., Evangelista L.R., Lenzi M.K., et al. Solutions for a non-Markovian diffusion equation. Phys. Lett. A, 2010, vol. 374, iss. 41, pp. 4193–4198. DOI: 10.1016/j.physleta.2010.08.049

[10] Morozov A.N., Skripkin A.V. Application of integral transforms to a description of the Brownian motion by a non-Markovian random process. Russ. Phys. J., 2009, vol. 52, iss. 2, pp. 184–195. DOI: 10.1007/s11182-009-9217-4

[11] Morozov A.N., Skripkin A.V. Spherical particle Brownian motion in viscous medium as non-Markovian random process. Phys. Lett. A, 2011, vol. 375, iss. 46, pp. 4113–4115. DOI: 10.1016/j.physleta.2011.10.001

[12] Morozov A.N., Skripkin A.V. Description of spherical liquid part evaporation as non-Markovian process using stochastic integral equations. Izvestiya vuzov. Fizika, 2010, no. 11-2, pp. 55–64 (in Russ.).

[13] Mura A., Taqqu M.S., Mainardi F. Non-Markovian diffusion equations and processes: analysis and simulations. Physica A, 2008, vol. 387, iss. 21, pp. 5033–5064. DOI: 10.1016/j.physa.2008.04.035

[14] Morozov A.N., Skripkin A.V. Propagation of heat in the space around a cylindrical surface as a non-Markovian random process. J. Eng. Phys. Thermophys., 2011, vol. 84, iss. 6, pp. 1201–1208. DOI: 10.1007/s10891-011-0585-6

[15] Lisy V., Tothova J., Glod L. On the correlation properties of thermal noise in fluids. Int. J. Thermophys., 2013, vol. 34, iss. 4, pp. 629–641. DOI: 10.1007/s10765-012-1290-1

[16] Morozov A.N., Skripkin A.V. Equilibrium temperature fluctuations of molecular and photonic gases in a spherical microcavity. Russ. Phys. J., 2012, vol. 55, iss. 7, pp. 736–747. DOI: 10.1007/s11182-012-9875-5

[17] Morozov A.N. Method for describing non-Markovian processes defined by a system of linear integral equations. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2017, no. 5, pp. 57–66 (in Russ.). DOI: 10.18698/1812-3368-2017-5-57-66

[18] Morozov A.N., Skripkin A.V. Nemarkovskie fizicheskie protsessy [Non-Markovian physical processes]. Moscow, Fizmatlit Publ., 2018.

[19] Morozov A.N. Preliminary results of recording the Kullback measure of voltage fluctuations on electrolytic cell. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2011, no. 2, pp. 16–24 (in Russ.).

[20] Bezrukov S.M., Irkhin A.I., Sibilev A.I. Verkhnyaya otsenka dlya intensivnosti 1/f-shuma elektrolitov: eksperimenty s molekulyarnymi kanalami [Upper estimate for intensity of electrolyte 1/f noise: experiments with molecular channels]. Preprint LIYaF-1190. Leningrad, LIYaF Publ., 1986 (in Russ.).

[21] Morozov A.N. Nonlocal influences of natural dissipative processes on the Kullback measure of voltage fluctuations on an electrolytic cell. NeuroQuantology, 2016, vol. 14, no. 3, pp. 477–483. DOI: 10.14704/nq.2016.14.3.920