Maximum Renyi entropy principle for systems with power-law Hamiltonians

The Renyi distribution ensuring the maximum of Renyi entropy is investigated for a particular case of a power-law Hamiltonian. Both Lagrange parameters alpha and beta can be eliminated. It is found that beta does not depend on a Renyi parameter q and can be expressed in terms of an exponent kappa of the power-law Hamiltonian and an average energy U. The Renyi entropy for the resulting Renyi distribution reaches its maximal value at q=1/(1+kappa) that can be considered as the most probable value of q when we have no additional information on the behavior of the stochastic process. The Renyi distribution for such q becomes a power-law distribution with the exponent -(kappa+1). When q=1/(1+kappa)+epsilon (0相似文献   

Classical mechanics and entropy

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Statistical mechanics of a dynamical system based on Conway's game of Life

We study a discrete dynamical system whose evolution is governed by rules similar to those of Conway's game of Life but also include a stochastic element (parametrized by a temperature). Statistical properties that are examined are density as a function of temperature and entropy (suitably defined). A phase transition and a certain thermodynamic constant of the motion are observed.Lady Davis Visiting Scientist at the Technion 1974–75.     

Statistical inference and entropy

We construct an entropy function such that statistical inference with respect to a partial measurement and a given a priori distribution is characterized by maximal entropy.     

Statistical mechanics of viscoelasticity

A unified treatment of viscoelasticity is developed in the framework of non-equilibrium classical statistical mechanics. An exact correspondence between Mori's continued-fractions formalism and rheological circuits is shown.     

Statistical mechanics of interfaces

On the basis of van der Waals theory for interfaces we evaluate explicitly the small-wavevector behavior of the pair correlation function along an interface. A correction to the density profile is also found. The results obtained are in full accord with capillary wave theory when wave amplitudes are regarded as small.     

Statistical systems with well-defined entropy

In this paper mathematical properties of local observables leading to well-defined entropy are discussed. Especially for the Bose-lattice-gas the finiteness and continuity of the local entropy is shown for every strong positive state.Talk given at the Symposium on Mathematical Methods in the Theory of Elementary Particles, Liblice castle, Czechoslovakia, June 18–23, 1978.     

Statistical mechanics of semiflexible polymers

We present the statistical-mechanical theory of semiflexible polymers based on the connection between the Kratky-Porod model and the quantum rigid rotator in an external homogeneous field, and treatment of the latter using the quantum mechanical propagator method. The expressions and relations existing for flexible polymers can be generalized to semiflexible ones, if one replaces the Fourier-Laplace transform of the end-to-end polymer distance, 1/(k ²/3 + p), through the matrix , where D and M are related to the spectrum of the quantum rigid rotator, and considers an appropriate matrix element of the expression under consideration. The present work provides also the framework to study polymers in external fields, and problems including the tangents of semiflexible polymers. We study the structure factor of the polymer, the transversal fluctuations of a free end of the polymer with fixed tangent of another end, and the localization of a semiflexible polymer onto an interface. We obtain the partition function of a semiflexible polymer in half space with Dirichlet boundary condition in terms of the end-to-end distribution function of the free semiflexible polymer, study the behaviour of a semiflexible polymer in the vicinity of a surface, and adsorption onto a surface.Received: 23 March 2004, Published online: 23 July 2004PACS: 36.20.-r Macromolecules and polymer molecules - 61.41. + e Polymers, elastomers, and plastics - 82.35.Gh Polymers on surfaces; adhesion     

Statistical mechanics of classical systems

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Statistical mechanics of superfluid models

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Statistical mechanics of relativistic plasmas

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Statistical mechanics of convex bodies

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