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p. 131149
Received: 26 February 2008 / Revised: 1 July 2008 / Accepted: 14 July 2008 / Published: 16 July 2008
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Abstract: A generalised notion of exponential families is introduced. It is based on the variational principle, borrowed from statistical physics. It is shown that inequivalent generalised entropy functions lead to distinct generalised exponential families. The wellknown result that the inequality of Cram´er and Rao becomes an equality in the case of an exponential family can be generalised. However, this requires the introduction of escort probabilities.
p. 150159
Published: 30 July 2008
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Abstract: Landauer’s principle is applied to information in the universe. Once stars began forming there was a constant information energy density as the increasing proportion of matter at high stellar temperatures exactly compensated for the expanding universe. The information equation of state was close to the dark energy value, w = 1, for a wide range of redshifts, 10 > z > 0.8, over one half of cosmic time. A reasonable universe information bit content of only 10^{87} bits is sufficient for information energy to account for all dark energy. A time varying equation of state with a direct link between dark energy and matter, and linked to star formation in particular, is clearly relevant to the cosmic coincidence problem. In answering the ‘Why now?’ question we wonder ‘What next?’ as we expect the information equation of state to tend towards w = 0 in the future.c
p. 160182
Received: 17 December 2007 / Revised: 30 July 2008 / Accepted: 30 July 2008 / Published: 14 August 2008
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Abstract: A rate equation for a discrete probability distribution is discussed as a route to describe smooth relaxation towards the maximum entropy distribution compatible at all times with one or more linear constraints. The resulting dynamics follows the path of steepest entropy ascent compatible with the constraints. The rate equation is consistent with the Onsager theorem of reciprocity and the fluctuationdissipation theorem. The mathematical formalism was originally developed to obtain a quantum theoretical unification of mechanics and thermodinamics. It is presented here in a general, nonquantal formulation as a part of an effort to develop tools for the phenomenological treatment of nonequilibrium problems with applications in engineering, biology, sociology, and economics. The rate equation is also extended to include the case of assigned timedependences of the constraints and the entropy, such as for modeling nonequilibrium energy and entropy exchanges.
p. 183199
Received: 28 July 2008 / Revised: 19 August 2008 / Accepted: 19 August 2008 / Published: 23 August 2008
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Abstract: The MaierSaupe model for binary mixtures of uniaxial discotic nematogens, formulated in a previous study [1], is used to compute and characterize orientational entropy [2] and orientational specific heat. These thermodynamic quantities are used to determine mixture type (ideal or nonideal) which arise due to their different intrinsic properties, determined by the molecular weight asymmetry ΔMw and the molecular interaction parameter β. These molecular properties are also used to characterize the critical concentration where the mixture behaves like a single component system and exhibits the minimum nematic to isotropic (NI) transition temperature (pseudopure mixture). A transition within the nematic phase takes place at this specific concentration. According to the MaierSaupe model, in a single mesogen, entropy at NI transition is a universal value; in this work we quantify the mixing effect on this universal property. The results and analysis provide a new tool to characterize molecular interaction and molecular weight differences in mesogenic mixtures using standard calorimetric measurements.
p. 200206
Received: 16 June 2008 / Revised: 14 August 2008 / Accepted: 18 August 2008 / Published: 25 August 2008
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Abstract: In this work, an analytical expression is developed for the differential entropy of a mixed Gaussian distribution. One of the terms is given by a tabulated function of the ratio of the distribution parameters.
p. 207223
Received: 24 June 2008 / Revised: 20 August 2008 / Accepted: 20 August 2008 / Published: 26 August 2008
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Abstract: Different equations have been proposed for estimating the glass transition temperature of amorphous mixtures. All such expressions lack a term to account for the effect of the entropy of mixing on the glass transition. An entropy based analysis for the glass transition of amorphous mixtures is presented. The treatment yields an explicit mixing term in the expression for the glass transition temperature of a mixture. The obtained expression reduces to the CouchmanKarasz equation in the limiting case where the contribution of the entropy of mixing approaches zero. Equivalent expressions are obtained for the glass transition temperature of a mixture of two glass formers as for the effect of a plasticizing liquid diluent on the glass transition temperature of an amorphous material.
p. 224239
Received: 30 June 2008 / Revised: 27 August 2008 / Accepted: 2 September 2008 / Published: 5 September 2008
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Abstract: The properties of an infinite system at a continuous phase transition are characterised by nontrivial critical exponents. These nontrivial exponents are related to scaling relations of the thermodynamic potential. The scaling properties of the singular part of the specific entropy of infinite systems are deduced starting from the wellestablished scaling relations of the Gibbs free energy. Moreover, it turns out that the corrections to scaling are suppressed in the microcanonical ensemble compared to the corresponding corrections in the canonical ensemble.
p. 240247
Received: 5 March 2008 / Revised: 25 August 2008 / Accepted: 25 August 2008 / Published: 19 September 2008
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Abstract: We explicitly obtain here a novel expression for the semiclassical Wehrl’s entropy using deformed algebras built up with the q¡coherent states (see Arik and Coon [J.Math.Phys. 17, 524 (1976) and Quesne [J. Phys. A 35, 9213 (2002)]). The generalization is investigated with emphasis on i) its behavior as a function of temperature and ii) the results obtained when the deformationparameter tends to unity.
p. 248260
Received: 31 July 2008 / Revised: 30 August 2008 / Accepted: 11 September 2008 / Published: 19 September 2008
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Abstract: We revisit the equilibrium properties of a classical onedimensional system of hardcore particles in the framework provided by the multiparticle correlation expansion of the configurational entropy. The vanishing of the cumulative contribution of morethantwoparticle correlations to the excess entropy is put in relation with the onset of a solidlike behavior at high densities.
p. 261273
Received: 1 September 2008 / Accepted: 12 September 2008 / Published: 19 September 2008
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Abstract: Axiomatic characterizations of Shannon entropy, Kullback Idivergence, and some generalized information measures are surveyed. Three directions are treated: (A) Characterization of functions of probability distributions suitable as information measures. (B) Characterization of set functions on the subsets of {1; : : : ;N} representable by joint entropies of components of an Ndimensional random vector. (C) Axiomatic characterization of MaxEnt and related inference rules. The paper concludes with a brief discussion of the relevance of the axiomatic approach for information theory.
p. 274284
Received: 24 July 2008 / Revised: 10 September 2008 / Accepted: 15 September 2008 / Published: 20 September 2008
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Abstract: A novel thermodynamic treatment of residual entropy in crystals, involving the configurational partition function, is suggested, which is consistent with both classical and statistical thermodynamics. It relates residual entropy to the inherent latent heat which would be released upon cooling if the reversible path were available. The nature of this heat is that if the crystal possessing residual entropy freezes above its Boltzmann’s characteristic temperature of molecular alignment, the difference in energy between different molecular arrangements is overcome by the kT heat bath to form a nearlyideal solution. However, upon cooling below this characteristic temperature, they would separate with a concomitant release of the corresponding energy, provided the reversible path were available.
p. 285308
Received: 8 August 2008 / Revised: 10 September 2008 / Accepted: 19 September 2008 / Published: 20 September 2008
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Abstract: We present a novel analytical method to calculate conformational entropy of ideal crosslinking polymers from the configuration integral by employing a Mayer series expansion. Mayerfunctions describing chemical bonds within the chain and for crosslinks are sharply peaked over the temperature range of interest, and, are well approximated as statistically weighted Dirac deltafunctions that enforce distance constraints. All geometrical deformations consistent with a set of distance constraints are integrated over. Exact results for a contiguous series of connected loops are employed to substantiate the validity of a previous phenomenological distance constraint model that describes protein thermodynamics successfully based on network rigidity.
p. 309318
Received: 17 May 2008 / Accepted: 9 September 2008 / Published: 24 September 2008
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Abstract: We have produced extended series for prudent selfavoiding walks on the square lattice. These are subsets of selfavoiding walks. We conjecture the exact growth constant and critical exponent for the walks, and show that the (anisotropic) generating function is almost certainly not differentiablyfinite.
p. 319333
Received: 3 May 2008 / Accepted: 4 September 2008 / Published: 24 September 2008
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Abstract: We discuss the different roles of the entropy principle in modern thermodynamics. We start with the approach of rational thermodynamics in which the entropy principle becomes a selection rule for physical constitutive equations. Then we discuss the entropy principle for selecting admissible discontinuous weak solutions and to symmetrize general systems of hyperbolic balance laws. A particular attention is given on the local and global wellposedness of the relative Cauchy problem for smooth solutions. Examples are given in the case of extended thermodynamics for rarefied gases and in the case of a multitemperature mixture of fluids.
p. 334364
Received: 31 July 2008 / Revised: 9 September 2008 / Accepted: 22 September 2008 / Published: 24 September 2008
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Abstract: Thermodynamic parameters of configurons – elementary excitations resulting from broken bonds in amorphous materials – are found from viscositytemperature relationships. Glassliquid transition phenomena and most popular models are described along with the configuron model of glass transition. The symmetry breaking, which occurs as a change of Hausdorff dimension of bonds, is examined at glassliquid transition. Thermal history effects in the glassliquid transition are interpreted in terms of configuron relaxation.
p. 365379
Received: 3 May 2008 / Accepted: 21 September 2008 / Published: 25 September 2008
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Abstract: The entropy evolution behaviour of a partial differential equation (PDE) in conservation form, may be readily discerned from the sign of the local source term of Shannon information density. This can be easily used as a diagnostic tool to predict smoothing and nonsmoothing properties, as well as positivity of solutions with conserved mass. The familiar fourth order diffusion equations arising in applications do not have increasing Shannon entropy. However, we obtain a new class of nonlinear fourth order diffusion equations that do indeed have this property. These equations also exhibit smoothing properties and they maintain positivity. The counterintuitive behaviour of fourth order diffusion, observed to occur or not occur on an apparently ad hoc basis, can be predicted from an easily calculated entropy production rate. This is uniquely defined only after a technical definition of the irreducible source term of a reaction diffusion equation.
p. 380390
Received: 3 May 2008 / Accepted: 4 September 2008 / Published: 25 September 2008
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Abstract: The fundamental optimization principle for nonequilibrium thermodynamics is given. The second entropy is introduced as the quantity that is maximised to determine the optimum state of a nonequilibrium system. In contrast, the principles of maximum or minimum dissipation, which have previously been proposed by Onsager, Prigogine, and others as the variational principle for such systems, are shown to be incapable of fulfilling that rôle.
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