Upper Bounded Current Fluctuations in One-Dimensional Driven Transport Systems

TL;DR

This paper proposes an upper bound on current fluctuations in one-dimensional driven transport systems, linking them to mean current and driving force, supported by theoretical proofs and numerical evidence.

Contribution

It introduces a universal upper bound on current fluctuations based on particle interactions, applicable across equilibrium and non-equilibrium systems, with rigorous proofs and simulations.

Findings

The upper bound is derived from a coarse-grained exchange model.

The inequality is rigorously proven for quantum ballistic transport.

Numerical evidence supports the bound in charged-particle transport.

Abstract

We conjecture that the current fluctuations in one-dimensional driven transport systems obey an upper bound determined by the mean current and the driving force. This inequality originates from repulsive interactions between transporting particles, and the bound is approached both in near-equilibrium systems and in far-from-equilibrium systems with weak interactions. We first propose a coarse-grained model describing random particle exchanges between two reservoirs with constant rates, from which the upper bound emerges. We then rigorously prove the inequality in quantum ballistic transport systems. Finally, we demonstrate its validity in two specific diffusive systems: the exclusion process, for which the inequality can be proven, and charged-particle transport, for which numerical evidence supports the inequality.