Abstract
In this paper, we consider the Langevin equation from an unusual point of view, that is as an archetype for a dissipative system driven out of equilibrium by an external excitation. Using path integral method, we compute exactly the probability density function of the power (averaged over a time interval of length τ) injected (and dissipated) by the random force into a Brownian particle driven by a Langevin equation. The resulting distribution, as well as the associated large deviation function, display strong asymmetry, whose origin is explained. Connections with the so-called “Fluctuation Theorem” are thereafter discussed. Finally, considering Langevin equations with a pinning potential, we show that the large deviation function associated with the injected power is completely insensitive to the presence of a potential.
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Farago, J. Injected Power Fluctuations in Langevin Equation. Journal of Statistical Physics 107, 781–803 (2002). https://doi.org/10.1023/A:1014538214117
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DOI: https://doi.org/10.1023/A:1014538214117