时空中的类平衡统计力学在远离平衡的确定性交通模型中
Equilibrium-like statistical mechanics in space-time for a deterministic traffic model far from equilibrium
AI总结：
本文提出了一种基于时空几何方法的确定性交通模型分析框架，通过高程函数描述系统动力学，推导出标度形式并恢复临界指数，揭示了远离平衡系统的物理机制。
摘要：
受之前关于时空阻塞中渗透似转变的数值证据启发，我们对确定性交通模型基本单元胞自动机规则184（ECA184）的瞬态动力学进行了分析描述。通过利用动力学的确定性结构，我们将问题重新表述为一个直接从初始条件构造的高程函数，从而在晶格配置上获得类似平衡统计力学的描述。这种表述允许在时空中的宏观可观测量，如总阻塞延迟和阻塞弛豫时间，以及微观的阻塞统计，用高程函数的几何性质来表达。由此我们推导出相关的标度形式，并恢复了之前在数值研究中观察到的临界指数。我们讨论了这种时空几何方法的物理意义。
英文摘要：
Motivated by earlier numerical evidence for a percolation-like transition in space-time jamming, we present an analytic description of the transient dynamics of the deterministic traffic model elementary cellular automaton rule 184 (ECA184). By exploiting the deterministic structure of the dynamics, we reformulate the problem in terms of a height function constructed directly from the initial condition, and obtain an equilibrium statistical mechanics-like description over the lattice configurations. This formulation allows macroscopic observables in space-time, such as the total jam delay and jam relaxation time, as well as microscopic jam statistics, to be expressed in terms of geometric properties of the height function. We thereby derive the associated scaling forms and recover the critical exponents previously observed in numerical studies. We discuss the physical implications of this space-time geometric approach.
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