45 research outputs found

    Boltzmann-Shannon Entropy: Generalization and Application

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    The paper deals with the generalization of both Boltzmann entropy and distribution in the light of most-probable interpretation of statistical equilibrium. The statistical analysis of the generalized entropy and distribution leads to some new interesting results of significant physical importance.Comment: 5 pages, Accepted in Mod.Phys.Lett.

    Generalised-Lorentzian Thermodynamics

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    We extend the recently developed non-gaussian thermodynamic formalism \cite{tre98} of a (presumably strongly turbulent) non-Markovian medium to its most general form that allows for the formulation of a consistent thermodynamic theory. All thermodynamic functions, including the definition of the temperature, are shown to be meaningful. The thermodynamic potential from which all relevant physical information in equilibrium can be extracted, is defined consistently. The most important findings are the following two: (1) The temperature is defined exactly in the same way as in classical statistical mechanics as the derivative of the energy with respect to the entropy at constant volume. (2) Observables are defined in the same way as in Boltzmannian statistics as the linear averages of the new equilibrium distribution function. This lets us conclude that the new state is a real thermodynamic equilibrium in systems capable of strong turbulence with the new distribution function replacing the Boltzmann distribution in such systems. We discuss the ideal gas, find the equation of state, and derive the specific heat and adiabatic exponent for such a gas. We also derive the new Gibbsian distribution of states. Finally we discuss the physical reasons for the development of such states and the observable properties of the new distribution function.Comment: 13 pages, 1 figur

    Average Entropy of a Subsystem from its Average Tsallis Entropy

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    In the nonextensive Tsallis scenario, Page's conjecture for the average entropy of a subsystem[Phys. Rev. Lett. {\bf 71}, 1291(1993)] as well as its demonstration are generalized, i.e., when a pure quantum system, whose Hilbert space dimension is mnmn, is considered, the average Tsallis entropy of an mm-dimensional subsystem is obtained. This demonstration is expected to be useful to study systems where the usual entropy does not give satisfactory results.Comment: Revtex, 6 pages, 2 figures. To appear in Phys. Rev.

    Steady shear flow thermodynamics based on a canonical distribution approach

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    A non-equilibrium steady state thermodynamics to describe shear flows is developed using a canonical distribution approach. We construct a canonical distribution for shear flow based on the energy in the moving frame using the Lagrangian formalism of the classical mechanics. From this distribution we derive the Evans-Hanley shear flow thermodynamics, which is characterized by the first law of thermodynamics dE=TdSQdγdE = T dS - Q d\gamma relating infinitesimal changes in energy EE, entropy SS and shear rate γ\gamma with kinetic temperature TT. Our central result is that the coefficient QQ is given by Helfand's moment for viscosity. This approach leads to thermodynamic stability conditions for shear flow, one of which is equivalent to the positivity of the correlation function of QQ. We emphasize the role of the external work required to sustain the steady shear flow in this approach, and show theoretically that the ensemble average of its power W˙\dot{W} must be non-negative. A non-equilibrium entropy, increasing in time, is introduced, so that the amount of heat based on this entropy is equal to the average of W˙\dot{W}. Numerical results from non-equilibrium molecular dynamics simulation of two-dimensional many-particle systems with soft-core interactions are presented which support our interpretation.Comment: 23 pages, 7 figure

    The imprints of superstatistics in multiparticle production processes

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    We provide an update of the overview of imprints of Tsallis nonextensive statistics seen in a multiparticle production processes. They reveal an ubiquitous presence of power law distributions of different variables characterized by the nonextensivity parameter q > 1. In nuclear collisions one additionally observes a q-dependence of the multiplicity fluctuations reflecting the finiteness of the hadronizing source. We present sum rules connecting parameters q obtained from an analysis of different observables, which allows us to combine different kinds of fluctuations seen in the data and analyze an ensemble in which the energy (E), temperature (T) and multiplicity (N) can all fluctuate. This results in a generalization of the so called Lindhard's thermodynamic uncertainty relation. Finally, based on the example of nucleus-nucleus collisions (treated as a quasi-superposition of nucleon-nucleon collisions) we demonstrate that, for the standard Tsallis entropy with degree of nonextensivity q < 1, the corresponding standard Tsallis distribution is described by q' = 2 - q > 1.Comment: 12 pages, 3 figures. Based on invited talk given by Z.Wlodarczyk at SigmaPhi2011 conference, Larnaka, Cyprus, 11-15 July 2011. To be published in Cent. Eur. J. Phys. (2011

    Gibbs' Paradox according to Gibbs and slightly beyond

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    The so-called Gibbs paradox is a paradigmatic narrative illustrating the necessity to account for the N! ways of permuting N identical particles when summing over microstates. Yet, there exist some mixing scenarios for which the expected thermodynamic outcome depends on the viewpoint one chooses to justify this combinatorial term. After a brief summary on Gibbs' paradox and what is the standard rationale used to justify its resolution, we will allow ourself to question from a historical standpoint whether the Gibbs paradox has actually anything to do with Gibbs' work. In so doing, we also aim at shedding a new light with regards to some of the theoretical claims surrounding its resolution. We will then turn to the statistical thermodynamics of discrete and continuous mixtures and introduce the notion of composition entropy to characterise these systems. This will enable us to address, in a certain sense, a "curiosity" pointed out by Gibbs in a paper published in 1876. Finally, we will �nish by proposing a connexion between the results we propose and a recent extension of the Landauer bound regarding the minimum amount of heat to be dissipated to reset one bit of memory
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