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1.
In this paper, we show a mathematical construction of Beck–Cohen superstatistics in the Bayesian point of view with the help of the two representations of a gamma function. Furthermore, it is shown how some results for superstatistics are related to each other. 相似文献
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A generalized entropy arising in the context of superstatistics is applied to an ideal gas. The curvature scalar associated to the thermodynamic space generated by this modified entropy is calculated using two formalisms of the geometric approach to thermodynamics. By means of the curvature/interaction hypothesis of the geometric approach to thermodynamic geometry it is found that as a consequence of considering a generalized statistics, an effective interaction arises but the interaction is not enough to generate a phase transition. This generalized entropy seems to be relevant in confinement or in systems with not so many degrees of freedom, so it could be interesting to use such entropies to characterize the thermodynamics of small systems. 相似文献
4.
We present the lowest order quantum correction to the semiclassical Boltzmann distribution function, and the equation satisfied
by this correction is given. Our equation for the quantum correction is obtained from the conventional quantum Boltzmann equation
by explicitly expressing the Planck constant in the gradient approximation, and the quantum Wigner distribution function is
expanded in powers of Planck constant, too. The negative quantum correlation in the Wigner distribution function which is
just the quantum correction terms is naturally singled out, thus obviating the need for the Husimi’s coarse grain averaging
that is usually done to remove the negative quantum part of the Wigner distribution function. We also discuss the classical
limit of quantum thermodynamic entropy in the above framework.
Supported by the National Natural Science Foundation of China (Grant No. 10404037) and the Scientific Research Fund of GUCAS
(Grant No. 055101BM03) 相似文献
5.
Z. Haba 《Physica A》2011,390(15):2776-2786
We obtain a non-linear generalization of the relativistic diffusion. We discuss diffusion equations whose non-linearity is a consequence of quantum statistics. We show that the assumptions of the relativistic invariance and an interpretation of the solution as a probability distribution substantially restrict the class of admissible non-linear diffusion equations. We consider relativistic invariant as well as covariant frame-dependent diffusion equations with a drift. In the latter case we show that there can exist stationary solutions of the diffusion equation besides the equilibrium solution corresponding to the quantum or Tsallis distributions. We define the relative entropy as a function of the diffusion probability and prove that it is monotonically decreasing in time when the diffusion tends to equilibrium. We discuss its relation to the thermodynamic behavior of diffusing particles. 相似文献
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We study the symmetry breaking of acoustic resonances measured by Ellegaard et al. (1996) [1] in quartz blocks. The observed resonance spectra show a gradual transition from a superposition of two uncoupled components, one for each symmetry realization, to a single component that is well represented by a Gaussian orthogonal ensemble (GOE) of random matrices. We discuss the applicability of superstatistical random-matrix theory to the final stages of the symmetry-breaking transition. A comparison is made between the formula from superstatistics and that from a previous work by Abd El-Hady et al. (2002) [7], which describes the same data by introducing a third GOE component. Our results suggest that the inverse chi-squared superstatistics could be used for studying the whole symmetry-breaking process. 相似文献
8.
Different advanced bridge function closures are utilized to investigate the structural and thermodynamic properties of dense Yukawa one-component plasma liquids within the framework of integral equation theory. The isomorph-based empirically modified hypernetted-chain, the variational modified hypernetted-chain, the Rogers–Young, and the Ballone–Pastore–Galli–Gazzillo approaches are compared at the level of thermodynamic properties, radial distribution functions, and bridge functions. The comparison, based on accuracy and computational speed, concludes that the two modified hypernetted-chain approaches are superior and singles out the isomorph-based variant as the most promising alternative to computer simulations of structural properties of dense Yukawa liquids. The possibility of further improvement through artificial crossover to exact asymptotic limits is studied. 相似文献
9.
《Physics letters. A》2020,384(21):126421
New formulas are given for the grand partition function of paraboson systems of order p with n orbitals and parafermion systems of order p with m orbitals. These formulas allow the computation of statistical and thermodynamic functions for such systems. We analyze and discuss the average number of particles on an orbital, and the average number of particles in the system. For some special cases (identical orbital energies, or equidistant orbital energies) we can simplify the grand partition functions and describe thermodynamic properties in more detail. Some specific properties are also illustrated in plots of thermodynamic functions. 相似文献
10.
In this article, we investigate the bound state solution of the Klein Gordon equation under mixed vector and scalar coupling of an energy-dependent deformed Hulthén potential in D dimensions. We obtain a transcendental equation after we impose the boundary conditions. We calculate energy spectra in four different limits and in arbitrary dimension via the Newton-Raphson method. Then, we use a statistical method, namely canonical partition function, and discuss the thermodynamic properties of the system in a comprehensive way. We find out that some of the thermodynamic properties overlap with each other, some of them do not. 相似文献
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We formulate binary fragmentation as a discrete stochastic process in which an integer mass k splits into two integer fragments j, , with rate proportional to the fragmentation kernel . We construct the ensemble of all distributions that can form in fixed number of steps from initial mass M and obtain their probabilities in terms of the fragmentation kernel. We obtain its partition function, the mean distribution and its evolution in time, and determine its stability using standard thermodynamic tools. We show that shattering is a phase transition that takes place when the stability conditions of the partition function are violated. We further discuss the close analogy between shattering and gelation, and between fragmentation and aggregation in general. 相似文献
12.
《Physica A》2006,361(1):41-54
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis invariant but the matrix elements are not statistically independent. Spectral characteristics of the mixed systems are expressed by averaging the corresponding quantities in the standard random-matrix theory over the fluctuations of the inverse variance of the matrix elements. We obtain analytical expressions for the level density and the nearest-neighbor-spacing distributions for four different inverse-variance distributions. The resulting expressions agree with each other for small departures from chaos, measured by an effective non-extensivity parameter. Our results suggest, among other things, that superstatistics is suited only for the initial stage of transition from chaos to regularity. 相似文献
13.
V. V. Ryazanov 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,72(4):629-639
A family of non-equilibrium statistical operators
is introduced which differ by the system age distribution
over which the quasi-equilibrium (relevant) distribution is
averaged. To describe the nonequilibrium states of a system we introduce a
new thermodynamic parameter – the lifetime of a system.
Superstatistics, introduced in works of Beck and Cohen [Physica A 322, 267 (2003)] as
fluctuating quantities of intensive thermodynamical parameters,
are obtained from the statistical distribution of lifetime (random
time to the system degeneracy) considered as a thermodynamical parameter. It
is suggested to set the mixing distribution of the fluctuating
parameter in the superstatistics theory in the form of the
piecewise continuous functions. The distribution of lifetime in
such systems has different form on the different stages of
evolution of the system. The account of the past stages of the evolution of a system
can have a substantial impact on the non-equilibrium behaviour of the system
in a present time moment. 相似文献
14.
We obtain the properties of a mean-field spin-glass (in which the bonds connecting each spin to every other spin are “frozen-in” with random signs), by locating the zeros of the partition function in the complex T plane. For N = 5 and 9 spins, we obtain the relevant polynomials and zeros explicitly, and the resulting thermodynamic properties (free energy, specific heat, magnetic susceptibility, etc.). We then analyze the properties of such a system in the thermodynamic limit N → ∞, where it is impossible to obtain the polynomials directly but where the presumed location of the zeros can be usefully construed. In this limit, the thermodynamic functions are obtainable as functions of the distribution functions of monopoles, quadrupoles, and possibly higher-order poles. 相似文献
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A non-extensive statistical physics approach to the polarity reversals of the geomagnetic field 总被引:2,自引:0,他引:2
Filippos Vallianatos 《Physica A》2011,390(10):1773-1778
Using the CK95 database of Cande and Kent (1995) [7], we apply the concepts of non-extensive statistical physics (NESP) to the time intervals between two consecutive geomagnetic reversals, called inter-reversal times. The application of NESM is appropriate to systems such as the geomagnetic field where non-linearity, long-range interactions, memory effects and scaling are important. We calculate the probability density function for the inter-reversal times and using the CK95 geomagnetic reversals and we estimate a thermodynamic q parameter of q=1.5, which supports the conclusion that the geomagnetic system is a sub-extensive one with long-range memory effects. The results discussed using the complementary to the NESP approach of superstatistics which is based on a superposition of ordinary local equilibrium statistical mechanics, using a suitable intensive parameter β that fluctuates on a relatively large temporal scale, leading to the conclusion that two degrees of freedom describe the process which generates the geomagnetic reversals. 相似文献
17.
We discuss the asymptotic behavior of thermodynamic functions in the vicinity of critical points on the basis of the theory of thermodynamic equilibrium stability. We obtain two types of relations between critical exponents in the critical state. The general thermodynamic results are illustrated using classic self-consistent Van der Waals and Curie-Weiss field models.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 58–63, October, 1987. 相似文献
18.
Hideo Hasegawa 《Physica A》2009,388(14):2781-2792
Magnetic and thermodynamical properties of itinerant-electron (metallic) ferromagnets described by the Hubbard model have been discussed with the use of the generalized Fermi-Dirac (GFD) distribution for nonextensive quantum systems. We have derived the GFD distribution within the superstatistics, which is equivalent to that obtained by the maximum-entropy method to the Tsallis entropy with the factorization approximation. By using the Hartree-Fock approximation to the electron-electron interaction in the Hubbard model, we have calculated magnetic moment, energy, specific heat and Curie-Weiss-type spin susceptibility, as functions of the temperature and entropic index q expressing the degree of the nonextensivity: q=1.0 corresponds to the Boltzmann-Gibbs statistics. It has been shown that by increasing the nonextensivity of |q−1|, the temperature dependence of magnetic moment becomes more significant and the low-temperature electronic specific heat is very much increased. This is attributed to enlarged Stoner excitations in the GFD distribution, which is elucidated by an analysis with the use of the generalized Sommerfeld expansion. We discuss the difference and similarity between the effects of the nonextensivity on metallic and insulating ferromagnets. 相似文献
19.
We localize a previously established nonlocal BRST invariance of the Gribov–Zwanziger (GZ) action by the introduction of additional fields. We obtain a modified GZ action with a corresponding local, albeit not nilpotent, BRST invariance. We show that correlation functions of the original elementary GZ fields do not change upon evaluation with the modified partition function. We discuss that for vanishing Gribov mass, we are brought back to the original Yang–Mills theory with standard BRST invariance. 相似文献