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31.
《Physics and Chemistry of Liquids》2012,50(2):177-188
Two and three-body correlation entropies of model fluids, in which particles interact each other through the 4th, 6th, 9th and 12th-inverse-power potentials, were calculated from their atomic configurations obtained by molecular dynamics simulations at their freezing points. Besides the soft-core fluid model with the inverse-power potentials, hard-sphere and classical one-component plasma models were employed to provide a comparison with the entropies of the soft-core model. The correlation entropies were plotted as a function of the softness of the potential. These values were also compared with the excess entropies of the hard-sphere and the one-component plasma models at their freezing points. 相似文献
32.
Robert H. Swendsen 《Physica A》2010,389(15):2898-2901
Although Ludwig Boltzmann was one of the primary founders of the field of statistical mechanics, very few contemporary physicists have actually read his papers. As a result, some of his ideas have been distorted or even lost over the course of time. In this paper, I will discuss some of the reasons for the neglect of Boltzmann’s writings and try to reintroduce one of his most important ideas, the definition of entropy. 相似文献
33.
34.
Jeff Kahn 《Proceedings of the American Mathematical Society》2002,130(2):371-378
For -regular, -vertex bipartite graphs with bipartition , a precise bound is given for the sum over independent sets of the quantity . (In other language, this is bounding the partition function for certain instances of the hard-core model.) This result is then extended to graded partially ordered sets, which in particular provides a simple proof of a well-known bound for Dedekind's Problem given by Kleitman and Markowsky in 1975.
35.
Manfred Einsiedler Douglas Lind 《Transactions of the American Mathematical Society》2004,356(5):1799-1831
We investigate algebraic -actions of entropy rank one, namely those for which each element has finite entropy. Such actions can be completely described in terms of diagonal actions on products of local fields using standard adelic machinery. This leads to numerous alternative characterizations of entropy rank one, both geometric and algebraic. We then compute the measure entropy of a class of skew products, where the fiber maps are elements from an algebraic -action of entropy rank one. This leads, via the relative variational principle, to a formula for the topological entropy of continuous skew products as the maximum of a finite number of topological pressures. We use this to settle a conjecture concerning the relational entropy of commuting toral automorphisms.
36.
Tai-PingLiu TommasoRuggeri 《应用数学学报(英文版)》2003,19(1):1-12
In shock wave theory there are two considerations in selecting the physically relevant shock waves.There is the admissibility criterion for the well-posedness of hyperbolic conservation laws.Another consideraztion concerns the entropy production across the shochs.The latter is natural from the physical point of view,but is not sufficient in its straightforward formulation,if the system is not genuinely nonlinear.In this paper we propose the principles of increasing entropy production and that of the superposition of shocks.These principles arc shown to be equivalent to the admissibility criterion. 相似文献
37.
Jean E. Burns 《Foundations of Physics》2007,37(12):1727-1737
Vacuum radiation causes a particle to make a random walk about its dynamical trajectory. In this random walk the root mean
square change in spatial coordinate is proportional to t
1/2, and the fractional changes in momentum and energy are proportional to t
−1/2, where t is time. Thus the exchange of energy and momentum between a particle and the vacuum tends to zero over time. At the end of
a mean free path the fractional change in momentum of a particle in a gas is very small. However, at the end of the mean free
path each particle undergoes an interaction that magnifies the preceding change, and the net result is that the momentum distribution
of the particles in a gas is randomized in a few collision times. In this way the random action of vacuum radiation and its
subsequent magnification by molecular interaction produces entropy increase. This process justifies the assumption of molecular
chaos used in the Boltzmann transport equation. 相似文献
38.
We explain the (non-)validity of close-to-equilibrium entropy production principles in the context of linear electrical circuits.
Both the minimum and the maximum entropy production principles are understood within dynamical fluctuation theory. The starting
point are Langevin equations obtained by combining Kirchoff’s laws with a Johnson-Nyquist noise at each dissipative element
in the circuit. The main observation is that the fluctuation functional for time averages, that can be read off from the path-space
action, is in first order around equilibrium given by an entropy production rate.
That allows to understand beyond the schemes of irreversible thermodynamics (1) the validity of the least dissipation, the
minimum entropy production, and the maximum entropy production principles close to equilibrium; (2) the role of the observables’
parity under time-reversal and, in particular, the origin of Landauer’s counterexample (1975) from the fact that the fluctuating
observable there is odd under time-reversal; (3) the critical remark of Jaynes (1980) concerning the apparent inappropriateness
of entropy production principles in temperature-inhomogeneous circuits. 相似文献
39.
Aladdin Shamilov 《Physica A》2007,382(2):465-472
In the present study we have formulated a generalization of entropy optimization problems (GEOP), proposed sufficient conditions for the existence of solution. We have suggested also a new method based on a priori evaluations and Newton's methods for calculation of Langrange multipliers. Mentioned method allows calculating Langrange multipliers by starting from arbitrary initial point for Newton's approximations of constructed auxiliary equation. The solution of auxiliary equation is chosen as initial point for second constructed auxiliary equation. The recurring mentioned process for finite time leads to achieve an initial point for Newton's approximations of given equation and allows to find its unknown solution. 相似文献
40.