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.

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• Classical statistical mechanics
• Nonequilibrium lattice models
• Langevin algorithm