Related papers: Entropy as a measure of diffusion

A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…

Existence of an entropy current with non-negative divergence puts a lot of constraints on the transport coefficients of a fluid, so does the existence of equilibrium. In all the cases we have studied so far we have seen an overlap between…

The concept of entropy in statistical physics is related to the existence of irreversible macroscopic processes. In this work, we explore a recently introduced entropy formula for a class of stochastic processes with more than one absorbing…

Entropy production is often interpreted as a proxy for microscopic disorder or environmental roughness in stochastic systems. We test this interpretation using controlled simulations of overdamped stochastic dynamics on curved surfaces in…

In reliability theory and survival analysis, the residual entropy is known as a measure suitable to describe the dynamic information content in stochastic systems conditional on survival. Aiming to analyze the variability of such…

The principle of entropy increase is not only the basis of statistical mechanics, but also closely related to the irreversibility of time, the origin of life, chaos and turbulence. In this paper, we first discuss the dynamic system…

We introduce the notion of relative volume entropy for two spacetimes with preferred compact spacelike foliations. This is accomplished by applying the notion of Kullback-Leibler divergence to the volume elements induced on spacelike…

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…

Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…

Based on the q-exponential distribution which has been observed in more and more physical systems, the varentropy method is used to derive the uncertainty measure of such an abnormal distribution function. The uncertainty measure obtained…

The rate of entropy production provides a useful quantitative measure of a non-equilibrium system and estimating it directly from time-series data from experiments is highly desirable. Several approaches have been considered for stationary…

Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…

A novel principle is presented which allows for the proof of bounded weak solutions to a class of physically relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure. The main feature of these systems is that…

We employ the relative entropy as a measure to quantify the difference of eigenmodes between Hermitian and non-Hermitian systems in elliptic optical microcavities. We have found that the average value of the relative entropy in the range of…

It is always some constraint that yields any nontrivial structure from statistical averages. As epitomized by the Boltzmann distribution, the energy conservation is often the principal constraint acting on mechanical systems. Here, we…

Here we present an analytic approximation for the entropy of floating-point numbers, along with bounds on the error of this approximation. It is well-known that the differential entropy is tightly linked to the discrete entropy of a…

Entropy rate of sequential data-streams naturally quantifies the complexity of the generative process. Thus entropy rate fluctuations could be used as a tool to recognize dynamical perturbations in signal sources, and could potentially be…

Fluid mixing usually involves the interplay between advection and diffusion, which together cause any initial distribution of passive scalar to homogenize and ultimately reach a uniform state. However, this scenario only holds when the…

The science of thermodynamics was put together in the Nineteenth Century to describe large systems in equilibrium. One part of thermodynamics defines entropy for equilibrium systems and demands an ever-increasing entropy for non-equilibrium…

In this paper we revisit the concept of mobility entropy. Over time, the structure of spatial interactions among urban centres tends to become more complex and evolves from centralised models to more scattered origin and destination…