arXiv subjects

Aryaman Jha

Publications and source records attributed to Aryaman Jha.

3 recordsLinked to original sources

arXiv2026

Equilibrium-like statistical mechanics in space-time for a deterministic traffic model far from equilibrium

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.

cond-mat.stat-mech↗

arXiv2025

Universal Scaling Laws in Freeway Traffic

Traffic congestion, a daily frustration for millions and a multi-billion dollar drain on economies, has long resisted deep physical understanding. While simple theoretical models of traffic flow have suggested connections to critical phenomena and non-equilibrium universality, direct empirical validation is lacking. Using extensive, high-resolution vehicle trajectory data from the I-24 MOTION testbed, we show that traffic flow exhibits both a percolation phase transition that is self-organized critical and fluctuations consistent with the Kardar-Parisi-Zhang universality in 1+1 dimensions. This suggests that the complex and seemingly chaotic formation of traffic jams has predictable statistical properties, which opens new avenues in traffic science for developing advanced forecasting and management strategies grounded in universal scaling laws.

nlin.CD↗

arXiv2025

Evidence of Non-Equilibrium Critical Phenomena in a Simple Model of Traffic

We present a novel approach to understand vehicular traffic jams by studying a simple model, Elementary Cellular Automaton Rule 184 (ECA 184). Using key traffic observables, such as the total delay and relaxation time, as well as microscopic measures like delays and lifetimes of individual jams, we show how these quantities can fully characterize the system's behavior, revealing features analogous to those of a continuous phase transition. We exploit specific properties of ECA 184 to develop an efficient algorithm for calculating these observables numerically and introduce an auxiliary quantity, termed ''elementary jams'', which allows us to determine these observables. We discuss the implications of our results, highlighting connections to a potential field-theoretic description of traffic and suggest future application of these methods to more complex models. Supporting code can be found on: https://github.com/Aryaman-Jha/ECA_184_Critical

cond-mat.stat-mech↗