We develop a rigorous theory of hard-sphere dynamics in the kinetic regime, away from thermal equilibrium. In the low density limit, the empirical density obeys a law of large numbers and the dynamics is governed by the Boltzmann equation. Deviations from this behaviour are described by dynamical correlations, which can be fully characterized for short times. This provides both a fluctuating Boltzmann equation and large deviation asymptotics.

中文翻译：

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Boltzmann-Grad 极限中的涨落理论

我们在远离热平衡的动力学状态中发展了严格的硬球动力学理论。在低密度极限下，经验密度服从大数定律，动力学受玻尔兹曼方程控制。这种行为的偏差由动态相关性描述，可以在短时间内完全表征。这提供了波动的玻尔兹曼方程和大偏差渐近线。