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  • Open Access

Hydrodynamic fluctuations of stochastic charged cellular automata

Takato Yoshimura1,2,* and Žiga Krajnik3,†

  • 1All Souls College, Oxford OX1 4AL, United Kingdom
  • 2Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom
  • 3Department of Physics, New York University, 726 Broadway, New York, New York 10003, USA

  • *Contact author: takato.yoshimura@physics.ox.ac.uk
  • †Contact author: ziga.krajnik@nyu.edu
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Phys. Rev. E 113, 064120 – Published 8 June, 2026

DOI: https://doi.org/10.1103/sjxq-hclt

Abstract

We study charge fluctuations of a family of stochastic charged cellular automata away from the deterministic single-file limit and obtain the exact typical charge probability distributions, known to be anomalous, using hydrodynamics. The cellular automata considered are examples of linearly degenerate systems where two distinct mechanisms of diffusion, namely, normal and convective diffusion, coexist. Our formalism, based on macroscopic fluctuation theory, allows us to describe current fluctuations stemming from these two diffusive processes, and we expect it to be applicable to generic linearly degenerate systems. The derived probability distributions match the exact microscopic result and numerical simulations.

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Phys. Rev. E 113, 064120– Published 8 June, 2026
  • Received 20 June 2025
  • Revised 30 March 2026
  • Accepted 15 April 2026
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