Large deviation functions

The Bias as a Large Deviation Function Glassy Dynamics... 

Section 11 introduces two examples, one from physics and the other from biology, that are paradigms of nonequilibrium behavior. Section in covers most important aspects of fluctuation theorems, whereas Section IV presents applications of fluctuation theorems to physics and biology. Section V presents the discipline of path thermodynamics and briefly discusses large deviation functions. Section VI discusses the topic of glassy dynamics from the perspective of nonequilibrium fluctuations in small cooperatively rearranging regions. We conclude with a brief discussion of future perspectives. 

A large deviation function P x) of a function Pl x) is defined if the following limit exists ... 

The bias defined in Eq. (103) is still another example of a large deviation function. Let us define the variable... 

In the following we show that Vn x) defines a large deviation function in the... 

J. L. Lebowitz and H. Spohn, A GaUavotti-Cohen type symmetry in the large deviation functional for stochastic dynamics. J. Stat. Phys. 95, 333-365 (1999). 

B. Derrida, J. L. Lebowitz, andE. R. Speer, Exact large deviation functional of a stationary open driven diffusive system the asymmetric exclusion process. J. Stat. Phys. 110, 775-810 (2003). 

C. Giardina, J. Kurchan, and L. Peliti, Direct evaluation of large-deviation functions. Phyi. Rev. Utt. 96, 120603 (2006). 

Giardina et alP point out the difficulty of testing or numerically predicting large deviation functions because they require sampling of rare events. A similar issue arises in testing the FRs. They devise a numerical procedure that allows the rare events to be sampled in a biased manner and therefore allow more efficient determination of the probability functions in the rare event regime. 

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