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The formalism of local maximization for entropy gradient producing the evolution and dynamical equations for closed systems. It eliminates the inconsistency between the reversibilty of time in dynamical equations and the strict direction of…
We prove that any asymptotics of a finite-dimensional quantum Markov processes can be formulated in the form of a generalized Jaynes principle in the discrete as well as in the continuous case. Surprisingly, we find that the open system…
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 propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied…
The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of…
The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added…
In this paper an alternative approach to statistical mechanics based on the maximum information entropy principle (MaxEnt) is examined, specifically its close relation with the Gibbs method of ensembles. It is shown that the MaxEnt…
A probabilistic rationale for I-divergence minimization (relative entropy maximization), non-parametric likelihood maximization and J-divergence minimization (Jeffres' entropy maximization) criteria is provided.
We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a…
A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems…
We examine the fundamental aspects of statistical mechanics, dividing the problem into a discussion purely about probability, which we analyse from a Bayesian standpoint. We argue that the existence of a unique maximising probability…
A well-known result across information theory, machine learning, and statistical physics shows that the maximum entropy distribution under a mean constraint has an exponential form called the Gibbs-Boltzmann distribution. This is used for…
I discuss the design of the method of entropic inference as a general framework for reasoning under conditions of uncertainty. The main contribution of this discussion is to emphasize the pragmatic elements in the derivation. More…
A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging…
The maximum entropy approach operating with quite general entropy measure and constraint is considered. It is demonstrated that for a conditional or parametrized probability distribution $f(x|\mu)$ there is a "universal" relation among the…
Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation.…
In this simple article, with possible applications in theoretical and applied physics, we suggest an original way to derive the expression of Shannon's entropy from a purely variational approach,using constraints. Based on the work of Edwin…
It is argued that the factorization of compound probability over subsystems is a consequence of the existence of thermodynamic equilibrium in the composite system having Tsallis entropy. So it should be respected by all exact calculations…
We consider a number of proposals for the entropy of sets of classical coarse-grained histories based on the procedures of Jaynes, and prove a series of inequalities relating these measures. We then examine these as a function of the…
Gibbs' theorem, which is originally intended for canonical ensembles with complete statistics has been generalized to open systems with incomplete statistics. As a result of this generalization, it is shown that the stationary equilibrium…