Geometric Universality of Currents

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.

15 pages, 5 figures

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Cited by in corpus (10)

• The Theory of Spin Noise Spectroscopy: A Review
• Geometric Heat Flux for Classical Thermal Transport in Interacting Open Systems
• No-pumping theorem for many particle stochastic pumps
• Occupation Probabilities and Fluctuations in the Asymmetric Simple Inclusion Process
• Stochastic Optimal Control as Non-equilibrium Statistical Mechanics: Calculus of Variations over Density and Current
• Fluctuation Relations for Current Components in Mesoscopic Electric Circuits
• Quantization and Fractional Quantization of Currents in Periodically Driven Stochastic Systems II: Full Counting Statistics
• Unification and new extensions of the no-pumping theorems of stochastic pumps
• Local structure of current fluctuations in diffusive systems beyond one dimension
• Stochastic Dynamics of Extended Objects in Driven Systems: I. Higher-Dimensional Currents in the Continuous Setting