This paper is an attempt to understand time-reversal asymmetry better by developing the quantitative description of that asymmetry. The aim is not to explain the asymmetry, but to describe it in more detail. Two model systems are considered here; one is the classical Lorentz gas, the other a quantum Lorentz gas. In the classical case, it is argued that the distribution of the directions of motion of particles that are about to hit an obstacle is qualitatitvely different from the analogous distribution for particles that have just hit the obstacle (an entropy-like functional of the velocity distribution function is used to characterize the asymmetry). In the quantum case, a similar distinction is drawn between the density matrix describing particles that have not yet encountered an obstacle and the one describing particles that have hit an obstacle or are in the process of doing so.

中文翻译：

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微观不可逆性：寻找时间不对称的微观描述

本文试图通过对时间反转不对称性进行定量描述来更好地理解时间反转不对称性。目的不是解释不对称性，而是更详细地描述它。这里考虑了两个模型系统；一种是经典洛伦兹气体，另一种是量子洛伦兹气体。在经典情况下，有人认为即将撞到障碍物的粒子的运动方向分布与刚刚撞到障碍物的粒子的类似分布（速度分布的类熵函数）有质的不同函数用于表征不对称性）。在量子情况下，