Related papers: Maximum entropy principle and the form of source i…
Different quantities that go by the name of entropy are used in variational principles to infer probability distributions from limited data. Shore and Johnson showed that maximizing the Boltzmann- Gibbs form of the entropy ensures that…
We define a one-parameter family of entropies, each assigning a real number to any probability measure on a compact metric space (or, more generally, a compact Hausdorff space with a notion of similarity between points). These entropies…
For a wide range of entropy measures, easy calculation of equilibria is possible using a principle of Game Theoretical Equilibrium related to Jaynes Maximum Entropy Principle. This follows previous work of the author and relates to works of…
Herding is a deterministic algorithm used to generate data points that can be regarded as random samples satisfying input moment conditions. The algorithm is based on the complex behavior of a high-dimensional dynamical system and is…
We present a general holistic theory for the organization of complex networks, both human-engineered and naturally-evolved. Introducing concepts of value of interactions and satisfaction as generic network performance measures, we show that…
The Principle of Maximum Entropy, a powerful and general method for inferring the distribution function given a set of constraints, is applied to deduce the overall distribution of 3D plasmoids (flux ropes/tubes) for systems where resistive…
In an essential and quite general setup, based on networks, we identify Schnakenberg's observables as the constraints that prevent a system from relaxing to equilibrium, showing that, in the linear regime, steady states satisfy a minimum…
Traditionally the exponential canonical distributions of Gibbsian statistical mechanics are given theoretical justification in at least four different ways: steepest descent method, counting method, Khinchin's method based on te central…
We consider the problem of estimating the population probability distribution given a finite set of multivariate samples, using the maximum entropy approach. In strict keeping with Jaynes' original definition, our precise formulation of the…
The problem of determining the joint probability distributions for correlated random variables with pre-specified marginals is considered. When the joint distribution satisfying all the required conditions is not unique, the "most unbiased"…
The phenomenon of entropy concentration provides strong support for the maximum entropy method, MaxEnt, for inferring a probability vector from information in the form of constraints. Here we extend this phenomenon, in a discrete setting,…
The lifetime of statistical system is introduced. It is supposed that the nonequilibrium statistical operator implicitly contains the lifetime. The operations of taking of invariant part, averaging on initial conditions used in works of…
The asymptotic behavior for entropy numbers of general Fourier multiplier operators of multiple series with respect to an abstract complete orthonormal system $\{\phi_{\textbf{m}}\}_{\textbf{m}\in \mathbb{N}^d_0}$ on a probability space and…
Given a sample of independent and identically distributed random variables, a novel nonparametric maximum entropy method is presented to estimate the underlying continuous univariate probability density function (pdf). Estimates are found…
We present a maximum entropy approach to analyze the internal dynamics of a small system in contact with a large bath e.g. a solute-solvent system. For the small solute, the fluctuations around the mean values of observables are not…
A family of non-equilibrium statistical operators (NSO) is introduced which differ by the system lifetime distribution over which the quasi-equilibrium (relevant) distribution is averaged. This changes the form of the source in the…
It is shown that the distribution derived from the principle of maximum Tsallis entropy is a superposable Levy-type distribution. Concomitantly, the leading order correction to the limit distribution is also deduced. This demonstration…
A theory for non-equilibrium systems is derived from a maximum entropy approach similar in spirit to the equilibrium theory given by Gibbs. Requiring Hamilton's principle of stationary action to be satisfied on average during a trajectory,…
Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…
The equilibrium distributions of probabilities providing maximality of Renyi and Tsallis entropies are rederived. New S-forms of them are found which are normalised with corresponding entropies in contrast to the usual Z-forms normalised…