Abstract According to the objective Bayesian approach inductive logic, premisses inductively entail a conclusion just when every probability function with maximal entropy, from all those that satisfy premisses, satisfies conclusion. When and are constraints on probabilities of sentences first-order predicate language, however, it is by no means obvious how determine these entropy functions. Thi...

Abstract Let $P_1,P_2,\dots , P_k$ be complex polynomials of degree at least two that are not simultaneously conjugate to monomials or Chebyshev polynomials, and $S$ the semigroup under composition generated by P_k$. We show all elements share a measure maximal entropy if only intersection principal left ideals $SP_1\cap SP_2\cap \dots \cap SP_k$ is non-empty.

It is shown that that the area law for the entropy of a quantum eld in a Kerr space-time is due to the quantum statistics with the maximal entropy principle. The entropies for one particle, a Boltzmann gas, a quantum mechanical gas obeying Bose-Einstein or Fermi-Dirac statistics, and a quantum eld in the Kerr space-time are calculated using the microcanonical ensemble approach and the brick wal...

We consider the following question: what is the least biased stochastic process over the runs of a given timed automaton? By “least biased”, we mean the one that generates runs with a distribution which is closest to uniform (w.r.t. volume). To answer this question, we first define stochastic processes over runs of timed automata and their entropy, the definition of which is inspired by Shannon...

Hawking's radiance, even as computed without account of backreaction, departs from blackbody form due to the mode dependence of the barrier penetration factor. Thus the radiation is not the maximal entropy radiation for given energy. By comparing estimates of the actual entropy emission rate with the maximal entropy rate for the given power, and using standard ideas from communication theory, w...

Maximization of the entropy rate is an important issue to design diffusion processes aiming at a well-mixed state. We demonstrate that it is possible to construct maximal-entropy random walks with only local information on the graph structure. In particular, we show that an almost maximal-entropy random walk is obtained when the step probabilities are proportional to a power of the degree of th...

We show that a certain type of conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also consider distribution asymptotics of information; e.g. for Boole’s transformation, information is asymptotically mod-normal, a property shared by certain ergodic, probability preserving transformations with zero entropy. §0 Intr...