Related papers: Entropy as a measure of diffusion

This paper is devoted to the use of the entropy and duality methods for the existence theory of reaction-cross diffusion systems consisting of two equations, in any dimension of space. Those systems appear in population dynamics when the…

Entropy and information can be considered dual: entropy is a measure of the subspace defined by the information constraining the given ambient space. Negative entropies, arising in na\"ive extensions of the definition of entropy from…

We define an entropy based on a chosen governing probability distribution. If a certain kind of measurements follow such a distribution it also gives us a suitable scale to study it with. This scale will appear as a link function that is…

We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces, give several techniques for computing lower bounds for it, and show that it is equal to a limit of…

Prompted by the realisation that the statistical entropy of an ideal gas in the micro-canonical ensemble should not fluctuate or change over time, the meaning of the H-theorem is re-interpreted from the perspective of information theory in…

It is shown that small, local disturbances of entropy in the atmosphere may give rise to "sound" waves propagating with a velocity which depends on the amplitude ratio of the local relative variations of temperature and volume. This…

In a glassy system different degrees of freedom have well-separated characteristic times, and are described by different temperatures. The stationary state is essentially non-equilibrium. A generalized statistical thermodynamics is…

The (measure-theoretical) entropy of a diffeomorphism along an expanding invariant foliation is the rate of complexity generated by the diffeomorphism along the leaves of the foliation. We prove that this number varies upper…

It is known that the ionic conductivity can be obtained by using the diffusion constant and the Einstein relation. We derive it here by extracting it from the steady electric current which we calculate in three ways, using statistics…

The quantum relative entropy is frequently used as a distance, or distinguishability measure between two quantum states. In this paper we study the relation between this measure and a number of other measures used for that purpose,…

Two identities in statistical mechanics involving entropy differences (or ratios of density of states) at constant energy are derived. The first provides a nontrivial extension of the Jarzynski equality to the microcanonical ensemble [C.…

Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth…

The past entropy is considered as an uncertainty measure for the past lifetime distribution. Generating function approach to entropy become popular in recent time as it generate several well-known entropy measures. In this paper, we…

We propose a new way to measure the balance between freedom and coherence in a dynamical system and a new measure of its internal variability. Based on the concept of entropy and ideas from neuroscience and information theory, we define…

The formulation of quantum mechanics within the framework of entropic dynamics includes several new elements. In this paper we concentrate on one of them: the implications for the theory of time. Entropic time is introduced as a…

Controversy exists regarding the possible existence of a transition between the liquid and glassy states of water. Here we use experimental measurements of the entropy, specific heat, and enthalpy of both liquid and glassy water to…

For a colloidal particle driven by a constant force across a periodic potential, we investigate the distribution of entropy production both experimentally and theoretically. For short trajectories, the fluctuation theorem holds…

We study the entropy production of a system with a finite number of states connected by random transition rates. The stationary entropy production, driven out of equilibrium both by asymmetric transition rates and by an external probability…

Dynamics, the study of change, is normally the subject of mechanics. Whether the chosen mechanics is ``fundamental'' and deterministic or ``phenomenological'' and stochastic, all changes are described relative to an external time. Here we…

For discrete-time stochastic processes, there is a close connection between return/waiting times and entropy. Such a connection cannot be straightforwardly extended to the continuous-time setting. Contrarily to the discrete-time case one…