# Fluctuation relations for anomalous dynamics

Source: [Fluctuation relations for anomalous dynamics](<https://www.sota2.com/research/paper/68fa23752c2a376019397e9c>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:52:31.334Z

Authors: A.V. Chechkin, R. Klages (2) \_\_INSTITUTION\_2\_\_ Institute for Theoretical Physics NSC KIPT, Kharkov, Ukraine, (2) Queen Mary University of London, School of Mathematical Sciences, London, UK)

Published: 2009-03-20T17:16:40.000Z

## Abstract

We consider work fluctuation relations (FRs) for generic types of dynamics generating anomalous diffusion: Levy flights, long-correlated Gaussian processes and time-fractional kinetics. By combining Langevin and kinetic approaches we calculate the probability distributions of mechanical and thermodynamical work in two paradigmatic nonequilibrium situations, respectively: a particle subject to a constant force and a particle in a harmonic potential dragged by a constant force. We check the transient FR for two models exhibiting superdiffusion, where a fluctuation-dissipation relation does not exist, and for two other models displaying subdiffusion, where there is a fluctuation-dissipation relation. In the two former cases the conventional transient FR is not recovered, whereas in the latter two it holds either exactly or in the long-time limit.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/0903.3571>)

[PDF](<https://arxiv.org/pdf/0903.3571.pdf>)