Path-ensemble averages in systems driven far from equilibrium

By Gavin E. Crooks. 1999

The Kawasaki nonlinear response relation, the transient fluctuation theorem, and the Jarzynski nonequilibrium work relation are all expressions that describe the behavior of a system that has been driven from equilibrium by an external perturbation. In contrast to linear response theory, these expressions are exact no matter the strength of the perturbation, or how far the system has been driven away from equilibrium. In this paper, I show that these three relations (and several other closely related results) can all be considered special cases of a single theorem. This expression is explicitly derived for discrete time and space Markovian dynamics, with the additional assumptions that the unperturbed dynamics preserve the appropriate equilibrium ensemble, and that the energy of the system remains finite.

Subfields: AI for Physical Sciences

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Variational Walkback: Learning a Transition Operator as a Stochastic Recurrent Net (2017, background): “By writing the distributions in terms of energies and free energies: , and p ( s 0 ) = e − [ E 0 ( s 0 ) − F 0 ] , one can see that the second term in the KL divergence is closely related to average heat dissipation in a ﬁnite time heating process (see e.g. (Crooks, 2000)).”
Relative Binding Free Energy Calculations in Drug Discovery: Recent Advances and Practical Considerations (2017, background): “44,45 All these implementations are related to each other, 46,47 but the latter has been suggested to be the most e ﬃ cient way 48 to conduct free energy calculations and appears to be the most widely used in practice.”
Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems (2008, methodology): “[42] Crooks, G. E., 1999, “Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences,” Phys.”
Training restricted Boltzmann machines: An introduction (2014, methodology): “So far, two estimation methods borrowed from statistical physics have been applied for estimating the partition function of RBMs: Salakhutdinov and Murray (2008) suggested to use AIS and Desjardins et al. (2011) employed BAR in combination with an importance sampling based estimator using samples fr”