816 research outputs found

    Horizon thermodynamics in f(R)f(R) theory

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    We investigate whether the new horizon first law proposed recently still work in f(R)f(R) theory. We identify the entropy and the energy of black hole as quantities proportional to the corresponding value of integration, supported by the fact that the new horizon first law holds true as a consequence of equations of motion in f(R)f(R) theories. The formulas for the entropy and energy of black hole found here are in agreement with the results obtained in literatures. For applications, some nontrivial black hole solutions in f(R)f(R) theories have been considered, the entropies and the energies of black holes in these models are firstly computed, which may be useful for future researches.Comment: 8 pages, no figur

    Relative Entropy and Inductive Inference

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    We discuss how the method of maximum entropy, MaxEnt, can be extended beyond its original scope, as a rule to assign a probability distribution, to a full-fledged method for inductive inference. The main concept is the (relative) entropy S[p|q] which is designed as a tool to update from a prior probability distribution q to a posterior probability distribution p when new information in the form of a constraint becomes available. The extended method goes beyond the mere selection of a single posterior p, but also addresses the question of how much less probable other distributions might be. Our approach clarifies how the entropy S[p|q] is used while avoiding the question of its meaning. Ultimately, entropy is a tool for induction which needs no interpretation. Finally, being a tool for generalization from special examples, we ask whether the functional form of the entropy depends on the choice of the examples and we find that it does. The conclusion is that there is no single general theory of inductive inference and that alternative expressions for the entropy are possible.Comment: Presented at MaxEnt23, the 23rd International Workshop on Bayesian Inference and Maximum Entropy Methods (August 3-8, 2003, Jackson Hole, WY, USA

    The Origin of 2 Sexes Through Optimization of Recombination Entropy Against Time and Energy

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    Sexual reproduction in Nature requires two sexes, which raises the question why the reproductive scheme did not evolve to have three or more sexes. Here we construct a constrained optimization model based on the communication theory to analyze trade-offs among reproductive schemes with arbitrary number of sexes. More sexes on one hand lead to higher reproductive diversity, but on the other hand incur greater cost in time and energy for reproductive success. Our model shows that the two-sexes reproduction scheme maximizes the recombination entropy-to-cost ratio, and hence is the optimal solution to the problem.Comment: 10 pages 5 figures. to appear in Bulletin of Mathematical Biolog

    Entropies from coarse-graining: convex polytopes vs. ellipsoids

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    We examine the Boltzmann/Gibbs/Shannon SBGS\mathcal{S}_{BGS} and the non-additive Havrda-Charv\'{a}t / Dar\'{o}czy/Cressie-Read/Tsallis \ Sq\mathcal{S}_q \ and the Kaniadakis Îş\kappa-entropy \ SÎş\mathcal{S}_\kappa \ from the viewpoint of coarse-graining, symplectic capacities and convexity. We argue that the functional form of such entropies can be ascribed to a discordance in phase-space coarse-graining between two generally different approaches: the Euclidean/Riemannian metric one that reflects independence and picks cubes as the fundamental cells and the symplectic/canonical one that picks spheres/ellipsoids for this role. Our discussion is motivated by and confined to the behaviour of Hamiltonian systems of many degrees of freedom. We see that Dvoretzky's theorem provides asymptotic estimates for the minimal dimension beyond which these two approaches are close to each other. We state and speculate about the role that dualities may play in this viewpoint.Comment: 63 pages. No figures. Standard LaTe
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