The universal principle that an open system can be driven to a state far from equilibrium, or organized, by strong negative entropy flow from its surroundings has been validated in numerous fields from physics and chemistry to the life science. In this paper, entropy flows for a severe storm are calculated via the entropy flow formula using the National Centers for Environmental Prediction/Nati...

Recently Verdù and Weissman introduced erasure entropies, which are meant to measure the information carried by one or more symbols given all of the remaining symbols in the realization of a random process or field. A natural relation to Gibbs measures has also been observed. In this short note we study this relation further, review a few earlier contributions from statistical mechanics, and pr...

For any C expanding map f of the circle we study the equilibrium states for the potential ψ = − log |f ′|. We formulate a C generalization of Pesin’s Entropy Formula that holds for all the SRB measures if they exist, and for all the (necessarily existing) SRB-like measures. In the C-generic case Pesin’s Entropy Formula holds for a unique SRB measure which is not absolutely continuous with respe...

We consider the entropy of systems of random transformations, where the transformations are chosen from the set of generators of a Z action. We show that the classical definition gives unsatisfactory entropy results in the higher-dimensional case, i.e. when d ≥ 2. We propose a new definition of the entropy for random group actions which agrees with the classical definition in the one-dimensiona...

In a recent article [4], Oh examined the impact of various key heuristics (e.g., deletion strategy, restart policy, decay factor, database reduction) in competitive SAT solvers. His key findings are that their expected success depends on whether the input formula is satisfiable or not. To further investigate these findings, we focused on two properties of satisfiable formulas: the entropy of th...

Recently, it has been proposed that the dimension of the Hilbert space of quantum gravity in deSitter space is finite and moreover it is expressed in terms of the coupling constants by using the entropy formula. A weaker conjecture would be that the coupling constant in deSitter space should take only discrete values not necessarily given by the entropy formula. We discuss quantization of the h...

In this work a relation between topology and thermodynamical features of gravitational instantons is shown. The expression for the Euler characteristic, through the Gauss–Bonnet integral, and the one for the entropy of gravitational instantons are proposed in a form that makes the relation between them self-evident. A new formulation of the Bekenstein–Hawking formula, where the entropy and the ...

The results of this paper generalize the formula for the entropy of a transfer function to time-varying systems. This is done through the use of some results on spectral factorizations due to Arveson and properties of theW-transform which generalizes the usual Ztransform for time-varying systems. Using the formula defined, it is shown that for linear fractional transformations like those that a...

The Sharma-Mittal entropies generalize the celebrated Shannon, Rényi and Tsallis entropies. We report a closed-form formula for the Sharma-Mittal entropies and relative entropies for arbitrary exponential family distributions. We instantiate explicitly the formula for the case of the multivariate Gaussian distributions and discuss on its estimation. PACS numbers: 03.65.Ta, 03.67.-a Submitted to...

We shall try to exhibit a relation between black hole entropy and topological entropy using the famous Baum-Connes conjecture for foliated manifolds which are particular examples of noncommutative spaces. Our argument is qualitative and it is based on the microscopic origin of the Beckenstein-Hawking area-entropy formula for black holes, provided by superstring theory, in the more general nonco...