Related papers: Maximum entropy principle and the form of source i…
This is a preliminary article stating and proving a new maximum entropy theorem. The entropies that we consider can be used as measures of biodiversity. In that context, the question is: for a given collection of species, which frequency…
The principle of maximum entropy (Maxent) is often used to obtain prior probability distributions as a method to obtain a Gibbs measure under some restriction giving the probability that a system will be in a certain state compared to the…
Exponential families form the backbone of modern statistics and machine learning, but textbooks seldom derive them from first principles in an accessible way. Although minimal sufficiency and the principle of maximum entropy, originating in…
The selection of an equilibrium state by maximising the entropy of a system, subject to certain constraints, is often powerfully motivated as an exercise in logical inference, a procedure where conclusions are reached on the basis of…
The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…
Using statistical thermodynamics, we derive a general expression of the stationary probability distribution for thermodynamic systems driven out of equilibrium by several thermodynamic forces. The local equilibrium is defined by imposing…
We present a new methodology for studying non-Hamiltonian nonlinear systems based on an information theoretic extension of a renormalization group technique using a modified maximum entropy principle. We obtain a rigorous dimensionally…
The form invariance of pseudoadditivity is shown to determine the structure of nonextensive entropies. Nonextensive entropy is defined as the appropriate expectation value of nonextensive information content, similar to the definition of…
We show that the principle of maximum entropy, a variational method appearing in statistical inference, statistical physics, and the analysis of stochastic dynamical systems, admits a geometric description from gauge theory. Using the…
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 investigate the maximum caliber variational principle as an inference algorithm used to predict dynamical properties of complex nonequilibrium, stationary, statistical systems in the presence of incomplete information. Specifically, we…
The Renyi distribution ensuring the maximum of a Renyi entropy is investigated for a particular case of a power--law Hamiltonian. Both Lagrange parameters, $\alpha$ and $\beta$ can be excluded. It is found that $\beta$ does not depend on a…
There has been interest in finding a general variational principle for non-equilibrium statistical mechanics. We give evidence that Maximum Caliber (Max Cal) is such a principle. Max Cal, a variant of Maximum Entropy, predicts dynamical…
A family of non-equilibrium statistical operators is introduced which differ by the system age distribution over which the quasi-equilibrium (relevant) distribution is averaged. To describe the nonequilibrium states of a system we introduce…
I show that the maximum entropy principle can be replaced by a more natural assumption, that there exists a phenomenological function of entropy consistent with the microscopic model. The requirement of existence provides then a unique…
We explore the use of the method of Maximum Entropy (ME) as a technique to generate approximations. In a first use of the ME method the "exact" canonical probability distribution of a fluid is approximated by that of a fluid of hard…
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…
Entropy estimation is of practical importance in information theory and statistical science. Many existing entropy estimators suffer from fast growing estimation bias with respect to dimensionality, rendering them unsuitable for…
The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively…
The main goal of this paper is to extend and apply the principle of maximum entropy (MaxEnt) to incomplete quantum process estimation tasks. We will define a so-called process entropy function being the von Neumann entropy of the state…