816 research outputs found
Horizon thermodynamics in theory
We investigate whether the new horizon first law proposed recently still work
in 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 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
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
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
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
We examine the Boltzmann/Gibbs/Shannon and the
non-additive Havrda-Charv\'{a}t / Dar\'{o}czy/Cressie-Read/Tsallis \
\ and the Kaniadakis -entropy \ \
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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