A generalized integral fluctuation theorem for general jump processes

Abstract

Using the Feynman-Kac and Cameron-Martin-Girsanov formulas, we obtain a generalized integral fluctuation theorem (GIFT) for discrete jump processes by constructing a time-invariable inner product. The existing discrete IFTs can be derived as its specific cases. A connection between our approach and the conventional time-reversal method is also established. Different from the latter approach that were extensively employed in existing literature, our approach can naturally bring out the definition of a time-reversal for a Markovian stochastic system. Intriguingly, we find the robust GIFT usually does not result into a detailed fluctuation theorem.

Two Refreshing Views of Fluctuation Theorems Through Kinematics Elements and Exponential Martingale

“…The Jarzynski equality (138) for this case was first proved for a one-dimensional diffusion process in [43]andthenforMarkov chains [15,37], general diffusion processes [11,62], and pure jump processes [63]. We seeherethattheseFR are true for general Markov processes, including stochastic equation with Poisson noise (52) or with Levy noise.…”

“…For the jump Langevin process (63), with the transition rates (64) for the Poisson noise, we can prove easily that the choice (83)i n( 76) is equivalent to the perturbation of the Hamiltonian according to H → H − k t O t .…”

“…Finally, these relations were put into the language of stochastic thermodynamics by Sekimoto [84]a n d Seifert [82]. There exist now many reviews on fluctuation relations in the Markovian context, like [42,51,63] for pure jump process or [10,11,51,58,62] for diffusion process, but the extension to FR for general Markov process is still under debate [6,89].…”

Mechanism for asymmetric bias in demonstrations of the NPI and fluctuation theorem

“…We can now calculate the expected range for each pair NPI by linearising Equation (25) and propagating the variance from the initial binomial distributions for each histogram bin. This is the standard error propagation method.…”

Nonequilibrium work equalities in isolated quantum systems

“…Hence, defining the irreversibility rather than pursuing the definition of the work shall be universal either in the classical systems or in the quantum systems. This idea has existed in the literature for long time [23,24,29,31,32,75,[86][87][88][89][90][91][92]. Here we use the idea to reobtain the equalities (2) and (4).…”