Why does time appear to pass irreversibly? To investigate, we introduce a class of partitioned cellular automata (PCAs) whose cellwise evolution is based on the chaotic baker's map. After imposing a suitable initial condition and restricting to a macroscopic view, we are left with a stochastic PCA (SPCA). When the underlying PCA's dynamics are reversible, the corresponding SPCA serves as a model of emergent time-reversal asymmetry. Specifically, we prove that its transition probabilities are homogeneous in space and time, as well as Markov relative to a Pearlean causal graph with timelike future-directed edges. Consequently, SPCAs satisfy generalizations of the second law of thermodynamics, which we term the Resource and Memory Laws. By subjecting information-processing agents (e.g., human experimenters) to these laws, we clarify issues regarding the Past Hypothesis, Landauer's principle, Boltzmann brains, scientific induction, and the so-called psychological arrow of time. Finally, by describing a theoretical agent powered by data compression, we argue that the algorithmic entropy takes conceptual precedence over both the Shannon-Gibbs and Boltzmann entropies.
翻译:时间似乎会不可逆地流过? 为了调查, 我们引入了一组分离的细胞自成一体的细胞自成一体( PCAs ), 其细胞进化以混乱的面包师的地图为基础。 因此, SPAs 满足了热动力学第二法的概括化, 我们称之为资源法和记忆法。 当基底的五氯苯甲醚的动态可以逆转时, 相应的SPCA会成为突发的时反反不对称的模型。 具体地说, 我们证明它的过渡概率在空间和时间上是均匀的, 相对于具有类似时间方向的未来边缘的珍珠因果图而言, Markov 。 因此, SPCAs 满足了热动力学第二法的概括化, 我们称之为资源法和记忆法。 通过让信息处理剂( 如人类实验者) 受这些法律的制约, 我们澄清了过去Hythes原则、 Landauer 原则、 Boltzmann 大脑、 科学感应变以及所谓的时间的心理箭头。 最后, 我们用数据压缩和Boltztrobtrobtrotrotis 来描述一个理论代理人, 我们论证法则都超越了。