Structure preserving properties of higher order moment closures for TASEP

TL;DR

This paper introduces a family of moment closure models for TASEP that preserve key structural properties, reducing complexity while maintaining probabilistic interpretation.

Contribution

It rigorously defines higher-order moment closures for TASEP, extending the Ribosome Flow Model and preserving fundamental properties of the master equation.

Findings

Models grow linearly with lattice size and exponentially with approximation order.

States retain probabilistic interpretation.

Structural properties of the master equation are preserved.

Abstract

The totally asymmetric simple exclusion process (TASEP) is a stochastic model for the unidirectional flow of interacting particles on a 1D-lattice that is much used in systems biology and statistical physics. Its master equation describes the evolution of the probability distribution on the configuration space. The size of the master equation grows exponentially with the length of the lattice. It is known that the complexity of the system may be reduced using mean-field approximations. We provide a rigorous definition of a family of such models using moments of any order and an extension to the pair approximation for obtaining closures for the system. The dimension of these models grows linearly with the lattice size and exponentially in the order of the approximation. Moreover, we show that the states of these models still have a probabilistic interpretation and that basic structural properties of the master equation are preserved. This extends known results on the Ribosome Flow Model which can be viewed as the first order approximation for TASEP.