Influence of flux balance on the generalized chemical potential in mass transport models

TL;DR

This paper explores how disorder and flux balance affect the measurement of generalized chemical potential in non-equilibrium mass transport systems, revealing that large-scale heterogeneities cause local measurements to differ from the global value.

Contribution

It demonstrates that geometrical heterogeneities impact local chemical potential measurements, while flux balance conditions still define a consistent global chemical potential.

Findings

Local disorder does not affect measurement accuracy.

Large-scale heterogeneities cause measurement discrepancies.

Global chemical potential remains well-defined despite local measurement issues.

Abstract

In equilibrium systems, the conservation of the number of particles (or mass) leads to the equalization of the chemical potential throughout the system. Using a non-equilibrium generalization of the notion of chemical potential, we investigate the influence of disorder and of the balance of mass fluxes on the generalized chemical potential in the framework of stochastic mass transport models. We focus specifically on the issue of local mesurements of the chemical potential. We find that while local dynamical disorder does not affect the measurement process, the presence of large-scale geometrical heterogeneities (branching geometry) leads to unequal local measurement results in different points of the system. We interpret these results in terms of mass flux balance, and argue that the conditions for the global definition of the chemical potential still hold, but that local measurements fail to capture the global theoretical value.