Related papers: Relative entropy and waiting times for continuous-…
In this work we introduce a method for estimating entropy rate and entropy production rate from finite symbolic time series. From the point of view of statistics, estimating entropy from a finite series can be interpreted as a problem of…
Fluctuation theorems make use of time reversal to make predictions about entropy production in many-body systems far from thermal equilibrium. Here we review the wide variety of distinct, but interconnected, relations that have been derived…
We prove the large deviation principle for several entropy and cross entropy estimators based on return times and waiting times on shift spaces over finite alphabets. We consider shift-invariant probability measures satisfying some…
Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…
Non-equilibrium fluctuations of various stochastic variables, such as work and entropy production, have been widely discussed recently in the context of large deviations, cumulants and fluctuation relations. Typically, one looks at the…
Estimating entropy production from real observation data can be difficult due to finite resolution in both space and time and finite measurement statistics. We characterize the statistical error introduced by finite sample size and compare…
Irreversibility is commonly quantified by entropy production. An external observer can estimate it through measuring an observable that is antisymmetric under time-reversal like a current. We introduce a general framework that, inter alia,…
We estimate the distance in total variation between the law of a finite state Markov process at time t, starting from a given initial measure, and its unique invariant measure. We derive upper bounds for the time to reach the equilibrium.…
We consider random walk with bounded jumps on a hypercubic lattice of arbitrary dimension in a dynamic random environment. The environment is temporally independent and spatially translation invariant. We study the rate functions of the…
The interrelationships of the fundamental biological processes natural selection, mutation, and stochastic drift are quantified by the entropy rate of Moran processes with mutation, measuring the long-run variation of a Markov process. The…
The entropy production rate is a key quantity in irreversible thermodynamics. In this work, we concentrate on the realization of entropy production rate in chemical reaction systems in terms of the experimentally measurable reaction rate.…
We establish convergence in the diffusive limit from entropy weak solutions of the equations of compressible gas dynamics with friction to the porous media equation away from vacuum. The result is based on a Lyapunov type of functional…
We show that under natural growth conditions on the entropy function, convergence in relative entropy is equivalent to $L_p$-convergence. The main tool is the theory of Young measures, in a form that accounts for the formation of…
The fluctuation theorem for entropy production is a remarkable symmetry of the distribution of produced entropy that holds universally in non-equilibrium steady states with Markovian dynamics. However, in systems with slow degrees of…
We use the $f-divergence$ also called relative entropy as a measure of diversity between probability densities and review its basic properties. In the sequence we define a few objects which capture relevant information from the sample of a…
Measuring entropy production of a system directly from the experimental data is highly desirable since it gives a quantifiable measure of the time-irreversibility for non-equilibrium systems and can be used as a cost function to optimize…
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…
Let $X$ be a discrete random variable with support $S$ and $f : S \to S^\prime$ be a bijection. Then it is well-known that the entropy of $X$ is the same as the entropy of $f(X)$. This entropy preservation property has been well-utilized to…
We study the statistics of infima, stopping times and passage probabilities of entropy production in nonequilibrium steady states, and show that they are universal. We consider two examples of stopping times: first-passage times of entropy…
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…