Ebtekar Aram, Hutter Marcus
Independent Researcher, Vancouver, BC V5Y 3J6, Canada.
Google DeepMind, London N1C 4AG, UK.
Entropy (Basel). 2024 Sep 10;26(9):776. doi: 10.3390/e26090776.
Why do we remember the past, and plan the future? We introduce a toy model in which to investigate emergent time asymmetries: the causal multibaker maps. These are reversible discrete-time dynamical systems with configurable causal interactions. Imposing a suitable initial condition or "Past Hypothesis", and then coarse-graining, yields a Pearlean locally causal structure. While it is more common to speculate that the other arrows of time arise from the thermodynamic arrow, our model instead takes the causal arrow as fundamental. From it, we obtain the thermodynamic and epistemic arrows of time. The epistemic arrow concerns records, which we define to be systems that encode the state of another system at another time, regardless of the latter system's dynamics. Such records exist of the past, but not of the future. We close with informal discussions of the evolutionary and agential arrows of time, and their relevance to decision theory.
我们为何能记住过去并规划未来？我们引入了一个用以研究涌现的时间不对称性的玩具模型：因果多面包师映射。这些是具有可配置因果相互作用的可逆离散时间动力系统。施加一个合适的初始条件或“过去假设”，然后进行粗粒化，会产生一种珀尔式的局部因果结构。虽然人们更常推测时间的其他箭头源自热力学箭头，但我们的模型反而将因果箭头视为基本的。由此，我们得到了时间的热力学箭头和认知箭头。认知箭头涉及记录，我们将其定义为在另一个时间编码另一个系统状态的系统，而不论后一个系统的动力学如何。这样的记录存在于过去，而不存在于未来。我们最后对时间的进化箭头和能动箭头进行了非正式讨论，以及它们与决策理论的相关性。
