Related papers: Conditional reversibility in nonequilibrium stocha…
The entropy production is commonly interpreted as measuring the distance from equilibrium. However, this explanation lacks a rigorous description due to the absence of a natural equilibrium measure. The present analysis formalizes this…
Filyokov and Karpov [Inzhenerno-Fizicheskii Zhurnal 13, 624 (1967)] have proposed a theory of non-equilibrium steady states in direct analogy with the theory of equilibrium states : the principle is to maximize the Shannon entropy…
For a stochastic process $(X_t)_{t\geq 0}$ we establish conditions under which the inverse first-passage time problem has a solution for any random variable $\xi >0$. For Markov processes we give additional conditions under which the…
The second law of thermodynamics states that entropy production in macroscopic systems is non-negative, reaching zero only at thermodynamic equilibrium. As a corollary, this implies that the state trajectory of macroscopic systems is…
The thermodynamic uncertainty relation, which establishes a universal trade-off between nonequilibrium current fluctuations and dissipation, has been found for various Markovian systems. However, this relation has not been revealed for…
We have shown recently that a Markov process conditioned on rare events involving time-integrated random variables can be described in the long-time limit by an effective Markov process, called the driven process, which is given…
Let $\{X_n\}$ be a stationary and ergodic time series taking values from a finite or countably infinite set ${\cal X}$. Assume that the distribution of the process is otherwise unknown. We propose a sequence of stopping times $\lambda_n$…
For stochastic non-equilibrium dynamics like a Langevin equation for a colloidal particle or a master equation for discrete states, entropy production along a single trajectory is studied. It involves both genuine particle entropy and…
We present an exact relationship between the entropy production and the distinguishability of a process from its time-reverse, quantified by the relative entropy between forward and backward states. The relationship is shown to remain valid…
As a fundamental thermodynamic principle, speed limits reveal the lower bound of entropy production (EP) required for a system to transition from a given initial state to a final state. While various speed limits have been developed for…
We introduce a continuous time-reversal operation which connects the time-forward and time-reversed trajectories in the steady state of an irreversible Markovian dynamics via a continuous family of stochastic dynamics. This continuous…
This paper studies time-inhomogeneous nonequilibrium diffusion processes, including both Brownian dynamics and Langevin dynamics. We derive upper bounds of the relative entropy production of the time-inhomogeneous process with respect to…
Motivated by entropic optimal transport, time reversal of diffusion processes is revisited. An integration by parts formula is derived for the carr\'e du champ of a Markov process in an abstract space. It leads to a time reversal formula…
We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive…
We study the multiple definitions of the entropy production for discrete-time Markov processes in single systems and composite systems. These definitions have been studied in single systems, but less so in composite systems. With a clear…
The following note proves that conditional entropy of a sequence is almost time-reversal invariant, specifically they only differ by a small constant factor dependent only upon the forward and backward models that the entropies are being…
Observing how long a dynamical system takes to return to some state is one of the most simple ways to model and quantify its dynamics from data series. This work proposes two formulas to estimate the KS entropy and a lower bound of it, a…
The relation between the thermodynamic entropy production and non-Markovian evolutions is matter of current research. Here, we study the behavior of the stochastic entropy production in open quantum systems undergoing unital non-Markovian…
In a time-reversal non-invariant system the entropy production, dS/dt, may be negative. Close to the critical point of medium it is positive: larger or smaller as compared with one above critical point depending on whether the transitions…
In this paper we revisit the notion of the "minus logarithm of stationary probability" as a generalized potential in nonequilibrium systems and attempt to illustrate its central role in an axiomatic approach to stochastic nonequilibrium…