相对论熵与相关的玻尔兹曼动力学
Relativistic Entropy and Related Boltzmann Kinetics
摘要：
在经典Boltzmman方程的碰撞积分中，两粒子关联函数的特殊形式唯一地确定了系统的熵，即Boltzmann-Gibbs-Shannon熵。在普通的相对论性玻尔兹曼方程中，通常进行一些标准的推广，关于它的经典版本，由狭义相对论强加的。这个方程的唯一组成部分是两粒子的关联函数，它默认地保持着它原来的经典形式，而这个事实也迫使相对论动力学也受玻尔兹曼-吉布斯-香农熵的支配。事实上，普通的相对论性玻尔兹曼方程承认指数Juttner分布是平稳的稳定分布。在这里，我们表明，狭义相对论定律和最大熵原理，建议一个相对论的推广也两个粒子的关联函数，然后熵。这样得到的，完全相对论性玻尔兹曼方程，遵守H-定理，并预测一个平稳的稳定分布，呈现幂律尾在高能量区。随后的相对论动力学理论保留了经典动力学的主要特征，在$c \to \infty$极限恢复。
英文摘要：
It is well known that the particular form of the two-particle correlation function, in the collisional integral of the classical Boltzmman equation, fix univocally the entropy of the system, which turn out to be the Boltzmann-Gibbs-Shannon entropy. In the ordinary relativistic Boltzmann equation, some standard generalizations, with respect its classical version, imposed by the special relativity, are customarily performed. The only ingredient of the equation, which tacitly remains in its original classical form, is the two-particle correlation function, and this fact imposes that also the relativistic kinetics is governed by the Boltzmann-Gibbs-Shannon entropy. Indeed the ordinary relativistic Boltzmann equation admits as stationary stable distribution, the exponential Juttner distribution. Here, we show that the special relativity laws and the maximum entropy principle, suggest a relativistic generalization also of the two-particle correlation function and then of the entropy. The so obtained, fully relativistic Boltzmann equation, obeys the H-theorem and predicts a stationary stable distribution, presenting power-law tails in the high energy region. The ensued relativistic kinetic theory preserves the main features of the classical kinetics, which recovers in the $c \to \infty$ limit.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
