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# Anomalous Transport and Fluctuation Relations: From Theory to Biology

Abstract:

I briefly remind of Langevin dynamics modeling Brownian motion including the role of fluctuation-dissipation relations. The latter become especially important when Langevin dynamics is generalized by using (power law) memory kernels for the friction coefficient and/or the noise. Such correlations make the dynamics nonMarkovian by typically generating anomalous transport in the form of anomalous diffusion, where the mean square displacement of an ensemble of particles grows nonlinearly for long times [1]. These Langevin models are tested for fluctuation relations generalizing the second law of thermodynamics to small systems in nonequilibrium [2]. I show that for generalized Langevin dynamics satisfying fluctuation-dissipation relations the conventional form of fluctuation relations is preserved while breaking fluctuation-dissipation relations leads to anomalous fluctuation relations violating the conventional form [3]. These generalized laws are observed in computer simulations of glassy dynamics and in experiments on biological cell migration.

[1] R. Klages, G.Radons, I.M.Sokolov (Eds.), Anomalous transport: foundations and applications. Wiley-VCH, Weinheim (2008)

[2] R.Klages, W.Just, C.Jarzynski (Eds.), Nonequilibrium Statistical Physics of Small Systems. Wiley-VCH, Weinheim (2013)

[3] A.V.Chechkin, F.Lenz, R.Klages, J.Stat.Mech. L11001 (2012); P.Dieterich, R.Klages, A.V.Chechkin, New J. Phys. 17, 075004 (2015)