论文标题
硬球气体的统计动力学：波动的玻尔兹曼方程和较大的偏差
Statistical dynamics of a hard sphere gas: fluctuating Boltzmann equation and large deviations
论文作者
论文摘要
我们提出了在玻尔兹曼（Boltzmann-Grad）限制中硬球体气体动力学波动的数学理论。我们证明：（1）从玻尔兹曼方程的溶液中的经验度量的波动，并用平均颗粒数的平方根缩放，收敛于由波动的玻尔兹曼方程驱动的高斯过程，如[67]中所预测的； （2）在平均粒子数量中，大偏差在定期假设下以大偏差的功能在[61]中以随机碰撞的动力学而在[61]中获得的大偏差表征。结果有效远离热平衡，但仅在短时间内有效。我们的策略基于累积生成函数的先验范围，表征了小相关性的精细结构。
We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that: (1) fluctuations of the empirical measure from the solution of the Boltzmann equation, scaled with the square root of the average number of particles, converge to a Gaussian process driven by the fluctuating Boltzmann equation, as predicted in [67]; (2) large deviations are exponentially small in the average number of particles and are characterized, under regularity assumptions, by a large deviation functional as previously obtained in [61] for dynamics with stochastic collisions. The results are valid away from thermal equilibrium, but only for short times. Our strategy is based on uniform a priori bounds on the cumulant generating function, characterizing the fine structure of the small correlations.
