An Example of Intrinsic Randomness in Deterministic PDEs

TL;DR

This paper introduces a novel mechanism linking the Totally Asymmetric Exclusion Process (TASEP) to an intrinsically stochastic weak solution of Burgers' equation, revealing how randomness naturally arises in deterministic PDEs through discrete stochastic processes.

Contribution

It demonstrates that TASEP can be interpreted as an intrinsically stochastic weak solution to Burgers' equation, highlighting a new source of randomness in deterministic PDEs.

Findings

TASEP corresponds to a stochastic weak solution of Burgers' equation.

Random jumps in TASEP induce intrinsic stochasticity in the PDE.

The mechanism explains how discrete stochastic effects manifest in continuum models.

Abstract

A new mechanism leading to a random version of Burgers' equation is introduced: it is shown that the Totally Asymmetric Exclusion Process in discrete time (TASEP) can be understood as an intrinsically stochastic, non-entropic weak solution of Burgers' equation on $\mathbb{R}$. In this interpretation, the appearance of randomness in the Burgers' dynamics is caused by random additions of jumps to the solution, corresponding to the random effects in TASEP.