The laws of Physics are time-reversible, making no qualitative distinction between the past and the future -- yet we can only go towards the future. This apparent contradiction is known as the `arrow of time problem'. Its resolution states that the future is the direction of increasing entropy. But entropy can only increase towards the future if it was low in the past, and past low entropy is a very strong assumption to make, because low entropy states are rather improbable, non-generic. Recent works, however, suggest we can do away with this so-called `past hypothesis', in the presence of reversible dynamical laws featuring expansion. We prove that this is the case for a toy model, set in a 1+1 discrete spacetime. It consists in graphs upon which particles circulate and interact according to local reversible rules. Some rules locally shrink or expand the graph. Generic states always expand; entropy always increases -- thereby providing a local explanation for the arrow of time.

翻译：物理定律是时间可逆的，在过去与未来之间没有质的区别——然而我们只能走向未来。这一明显矛盾被称为“时间箭头问题”。其解决方案指出，未来是熵增加的方向。但熵只有在过去处于低熵状态时才能向未来增加，而过去低熵是一个非常强的假设，因为低熵状态相当罕见且非典型。然而，近期研究表明，在存在膨胀特征的可逆动力学定律的情况下，我们可以摒弃这一所谓的“过去假设”。我们证明，对于设定在1+1维离散时空中的玩具模型，情况确实如此。该模型由粒子在图上根据局部可逆规则循环和相互作用的图构成。某些规则局部收缩或扩展图。通用状态始终膨胀；熵始终增加——从而为时间箭头提供了局部解释。