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首页> 外文期刊>Physica, A. Statistical mechanics and its applications >Finite and infinite dynamical systems of identical interacting particles
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Finite and infinite dynamical systems of identical interacting particles

机译：相同相互作用粒子的有限和无限动力学系统

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A dynamical system of infinite volume and of infinite number of identical interacting particles occupying energy levels e(i) (i = 1, 2,..., I) has been constructed as the limit of an infinite sequence of finite, equivalent systems of increasing size and particle number. Systems both in equilibrium and in non-equilibrium state (designated S-infinity = lim S-k, S-infinity* = lim S-k*, respectively, k = 1, 2....) were investigated. The main results are: (i) The values in the T-limit (thermodynamic limit) of the physical quantities characterizing these systems are determined. (ii) The time evolution process both in S-k* and in S-infinity* systems is governed by the non-linear rate equations p(i)(t)/dt = - ln p(i)(t) + a(t) + e(i)b(t) (i = 1, 2,..., I) with common initial conditions p(i)(t(0)), where p(i)(t) = n(i)(t)/N are the occupation probabilities at time t. The time evolution process in the S-k* and S-infinity* systems is the same. The asymptotic approach to the equilibrium state is proved. (iii) For the case of the equilibrium state, the Boltzmann probability distribution pi is given by the equation - ln p(i) +a +e(i)b = 0 common to S-k and S-infinity systems with the same value of a and b. The term a = beta(-1)a(e) where a(e) is the free energy per particle, and b = -beta (=-1/k(B)T). (iv) The conditions for the equivalence of the systems being in equilibrium and also of the ones in non-equilibrium are stated. (C) 2008 Elsevier B.V. All rights reserved.
机译：构造了一个无限体积的动态系统，并且无限数量的相同相互作用粒子占据了能级e（i）（i = 1，2，...，I），作为有限等效系统的无限序列的极限尺寸和颗粒数量的增加。研究了处于平衡和非平衡状态的系统（分别指定为S-infinity = lim S-k，S-infinity * = lim S-k *，k = 1、2 ...）。主要结果是：（i）确定表征这些系统的物理量的T极限（热力学极限）值。 （ii）Sk *和S-infinity *系统中的时间演化过程均由非线性速率方程p（i）（t）/ dt =-ln p（i）（t）+ a（t ）+ e（i）b（t）（i = 1，2，...，I）具有共同的初始条件p（i）（t（0）），其中p（i）（t）= n（i ）（t）/ N是在时间t的职业概率。 S-k *和S-infinity *系统中的时间演化过程是相同的。证明了达到平衡状态的渐近方法。 （iii）对于平衡态，玻尔兹曼概率分布pi由等式-ln p（i）+ a + e（i）b = 0给Sk和S-无穷大系统所共有，其等式为a和b。术语a = beta（-1）a（e），其中a（e）是每个粒子的自由能，b = -beta（= -1 / k（B）T）。 （iv）说明了处于平衡状态的系统和处于非平衡状态的系统的等价条件。 （C）2008 Elsevier B.V.保留所有权利。

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