We introduce a Kac’s type walk whose rate of binary collisions preserves the total momentum but not the kinetic energy. In the limit of large number of particles we describe the dynamics in terms of empirical measure and flow, proving the corresponding large deviation principle. The associated rate function has an explicit expression. As a byproduct of this analysis, we provide a gradient flow formulation of the Boltzmann-Kac equation.

中文翻译：

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Kac-Like Walks 的大偏差

我们引入了 Kac 类型的步行，其二元碰撞率保留了总动量但不保留动能。在大量粒子的限制下，我们根据经验测量和流动来描述动力学，证明了相应的大偏差原理。相关的速率函数有一个明确的表达式。作为此分析的副产品，我们提供了 Boltzmann-Kac 方程的梯度流公式。