Abstract
Motivated by the time behavior of the functional arising in the variational approach to the Kardar-Parisi-Zhang (KPZ) equation, and in order to study fluctuation theorems in such a system, we have adapted a path-integral scheme that adequately fits to this kind of study dealing with unstable systems. As the KPZ system has no stationary probability distribution, we show how to proceed for obtaining detailed as well as integral fluctuation theorems. This path-integral methodology, together with the variational approach, in addition to allowing analyze fluctuation theorems, can be exploited to determine a large deviation function for entropy production.
Highlights
The last few decades have witnessed a growing interest in diverse aspects of nonequilibrium systems
Motivated by the time behavior of the functional arising in the variational approach to the Kardar-Parisi-Zhang (KPZ) equation, and in order to study fluctuation theorems in such a system, we have adapted a path-integral scheme that adequately fits to this kind of study dealing with unstable systems
As the KPZ system has no stationary probability distribution, we show how to proceed for obtaining detailed as well as integral fluctuation theorems
Summary
The last few decades have witnessed a growing interest in diverse aspects of nonequilibrium systems. The second aspect refers to the so-called stochastic thermodynamics,[12–17,19,20] exploiting continuous (via Langevin-like equations) as well as discrete (via master equations) descriptions and approaches, where some recent review-like articles give a panoramic view of the field and the broad spectrum of fluctuation theorems that were obtained as well as of their possible applications.[21,22] Until very recently, these two aspects have not been analyzed together, that is, studies on the stochastic thermodynamics for the KPZ model are scarce.[23–25]. It is worth noting that such a PDF keeps memory of the initial condition (a fact that arises naturally within the variational approach[11]) Aspects of such a peculiar behavior were analyzed in Ref. 29 through the study of some toy models.
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