Geometric Universality of Currents

TL;DR

This paper reveals a geometric universality in the statistics of particle currents in non-equilibrium stochastic systems on networks, applicable across various natural and man-made processes, under conditions of constant relative rates.

Contribution

It introduces a symmetry principle leading to geometric universality of current statistics in stochastic network systems with constant relative rates.

Findings

Universal symmetry in particle current statistics

Applicable to diverse systems like internet queues and biological networks

Demonstrated through examples in mesoscopic physics and biochemistry

Abstract

We discuss a non-equilibrium statistical system on a graph or network. Identical particles are injected, interact with each other, traverse, and leave the graph in a stochastic manner described in terms of Poisson rates, possibly dependent on time and instantaneous occupation numbers at the nodes of the graph. We show that under the assumption of constancy of the relative rates, the system demonstrates a profound statistical symmetry, resulting in geometric universality of the statistics of the particle currents. This phenomenon applies broadly to many man-made and natural open stochastic systems, such as queuing of packages over the internet, transport of electrons and quasi-particles in mesoscopic systems, and chains of reactions in bio-chemical networks. We illustrate the utility of our general approach using two enabling examples from the two latter disciplines.