Large deviation functions are an essential tool in the statistics of rare events. Often they can be obtained by contraction from a so-called level 2 or level 2.5 large deviation functional characterizing the empirical density and current of the underlying stochastic process. For Langevin systems obeying detailed balance, the explicit form of the level 2 functional has been known ever since the mathematical work of Donsker and Varadhan. We rederive the Donsker-Varadhan result using stochastic path-integrals. We than generalize the derivation to level 2.5 large deviation functionals for non-equilibrium steady states and elucidate the relation between the large deviation functionals and different notions of entropy production in stochastic thermodynamics. Finally, we discuss some aspects of the contractions to level 1 large deviation functions and illustrate our findings with examples. T TIf the limit exists, the random variable a T is said to satisfy a large deviation principle [5]. The large deviation function ( ) J a contains the desired information about the statistics of a T . First of all, consistency requires á ñ = ( ) J a 0 st and ( )  J a 0 for all a. Taylor expansion around the minimum of ( ) J a up to second order yields a Gaussian probability distribution generalizing Einsteins theory of equilibrium fluctuations[ 7]. In addition, the complete function ( ) J a characterizes the statistics of exponentially rare realizations a T that deviate substantially from á ñ a st . Recent applications of large deviation functions to describe rare events in statistical mechanics can be found in [8][9][10][11][12][13][14].Different Brownian functionals deriving from the same stochastic process ( ) x t have different large deviation functions. On the other hand, we may rewrite (1.1) as New J. Phys. 18 (2016) 083010 J Hoppenau et al New J. Phys. 18 (2016) 083010 J Hoppenau et al New J. Phys. 18 (2016) 083010 J Hoppenau et al New J. Phys. 18 (2016) 083010 J Hoppenau et al

The typical values and fluctuations of time-integrated observables of nonequilibrium processes driven in steady states are known to be characterized by large deviation functions, generalizing the entropy and free energy to nonequilibrium systems. The definition of these functions involves a scaling limit, similar to the thermodynamic limit, in which the integration time τ appears linearly, unless the process considered has long-range correlations, in which case τ is generally replaced by τ^{ξ} with ξ≠1. Here, we show that such an anomalous power-law scaling in time of large deviations can also arise without long-range correlations in Markovian processes as simple as the Langevin equation. We describe the mechanism underlying this scaling using path integrals and discuss its physical consequences for more general processes.

We determine the complete asymptotic behaviour of the work distribution in driven stochastic systems described by Langevin equations. Special emphasis is put on the calculation of the pre-exponential factor which makes the result free of adjustable parameters. The method is applied to various examples and excellent agreement with numerical simulations is demonstrated. For the special case of parabolic potentials with time-dependent frequencies, we derive a universal functional form for the asymptotic work distribution.PACS. 0 5.70. Ln,

We characterize statistical properties of the flow field in developed turbulence using concepts from stochastic thermodynamics. On the basis of data from a free air-jet experiment, we demonstrate how the dynamic fluctuations induced by small-scale intermittency generate analogs of entropy-consuming trajectories with sufficient weight to make fluctuation theorems observable at the macroscopic scale. We propose an integral fluctuation theorem for the entropy production associated with the stochastic evolution of velocity increments along the eddy hierarchy and demonstrate its extreme sensitivity to the accurate description of the tails of the velocity distributions.