水库涨落引起的统计幂律和万有恒温器独立原理
Statistical Power Law due to Reservoir Fluctuations and the Universal Thermostat Independence Principle
摘要：
在固定的总能量下，粒子数的某些波动通过相空间体积比的诱导波动，精确地导致单粒子能量的截幂律分布。温度参数由均分关系自动表示，而q参数与标度方差和粒子数的期望值有关。对于二项分布，q较小，对于负二项分布，q大于1。这些结果也代表了一个近似的一般粒子数分布在水库中的正则展开的二阶。对于一般的系统，平均相空间体积比扩展到二阶提供了一个q参数的热容和温度的变化。然而，q不同于1导致玻尔兹曼-吉布斯熵的非加性。我们证明了一个变形熵，K（S），可以构造和使用的要求加性。这一要求导致了K（S）的二阶微分方程。最后，广义q-熵公式包含Tsallis，Renyi和Boltzmann-Gibbs-Shannon表达式作为特殊情况。对于发散的温度方差，我们得到了一个新的熵公式。
英文摘要：
Certain fluctuations in particle number at fixed total energy lead exactly to a cut-power law distribution in the one-particle energy, via the induced fluctuations in the phase-space volume ratio. The temperature parameter is expressed automatically by an equipartition relation, while the q-parameter is related to the scaled variance and to the expectation value of the particle number. For the binomial distribution q is smaller, for the negative binomial q is larger than one. These results also represent an approximation for general particle number distributions in the reservoir up to second order in the canonical expansion. For general systems the average phase-space volume ratio expanded to second order delivers a q parameter related to the heat capacity and to the variance of the temperature. However, q differing from one leads to non-additivity of the Boltzmann-Gibbs entropy. We demonstrate that a deformed entropy, K(S), can be constructed and used for demanding additivity. This requirement leads to a second order differential equation for K(S). Finally, the generalized q-entropy formula contains the Tsallis, Renyi and Boltzmann-Gibbs-Shannon expressions as particular cases. For diverging temperature variance we obtain a novel entropy formula.
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