Injected power fluctuations in Langevin equation

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 tau) 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.