Related papers: Generalized entropy optimized by an arbitrary dist…
We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…
We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…
Superstatistics describes nonequilibrium steady states as superpositions of canonical ensembles with a probability distribution of temperatures. Rather than assume a certain distribution of temperature, recently [J. Phys. A: Math. Theor.…
A strengthened version of the central limit theorem for discrete random variables is established, relying only on information-theoretic tools and elementary arguments. It is shown that the relative entropy between the standardised sum of…
For a Markovian dynamics on discrete states, the logarithmic ratio of waiting-time distributions between two successive, instantaneous transitions in forward and backward direction is a measure of time-irreversibility. It thus serves as an…
A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…
We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of states is convex but typically non-unique. The…
The entropy production of a nonequilibrium system with broken detailed balance is a random variable whose mean value is nonnegative. Among the total entropy production, the housekeeping entropy production is associated with the heat…
We generalize the usual exponential Boltzmann factor to any reasonable and potentially observable distribution function, $B(E)$. By defining generalized logarithms $\Lambda$ as inverses of these distribution functions, we are led to a…
We develop a maximum relative entropy formalism to generate optimal approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a…
We consider a measure $\psi$ k of dispersion which extends the notion of Wilk's generalised variance, or entropy, for a d-dimensional distribution, and is based on the mean squared volume of simplices of dimension k $\le$ d formed by k + 1…
We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to…
We apply a common measure of randomness, the entropy, in the context of iterated functions on a finite set with n elements. For a permutation, it turns out that this entropy is asymptotically (for a growing number of iterations) close to…
Systems with a long-term stationary state that possess as a spatio-temporally fluctuation quantity $\beta$ can be described by a superposition of several statistics, a "super statistics". We consider first, the Gamma, log-normal and…
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…
Starting from the geometrical interpretation of the R\'enyi entropy, we introduce further extensive generalizations and study their properties. In particular, we found the probability distribution function obtained by the MaxEnt principle…
Quantum uncertainty relations are formulated in terms of relative entropy between distributions of measurement outcomes and suitable reference distributions with maximum entropy. This type of entropic uncertainty relation can be applied…
We derive an Ito stochastic differential equation for entropy production in nonequilibrium Langevin processes. Introducing a random-time transformation, entropy production obeys a one-dimensional drift-diffusion equation, independent of the…
For regularized distributions we establish stability of the characterization of the normal law in Cramer's theorem with respect to the total variation norm and the entropic distance. As part of the argument, Sapogov-type theorems are…
The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems, by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and…