Current fluctuations at a phase transition

Abstract

The ABC model is a simple diffusive one-dimensional non-equilibrium system which exhibits a phase transition. Here we show that the cumulants of the currents of particles through the system become singular near the phase transition. At the transition, they exhibit an anomalous dependence on the system size (an anomalous Fourier's law). An effective theory for the dynamics of the single mode which becomes unstable at the transition allows one to predict this anomalous scaling.

7 pages; 3 figures

References in corpus (13)

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• Fluctuation theorems for stochastic dynamics
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Cited by in corpus (15)

• Universality in dynamical phase transitions of diffusive systems
• Landau theory for finite-time dynamical phase transitions
• Aging processes in systems with anomalous slow dynamics
• Ensemble inequivalence : Landau theory and the ABC model
• Assisted exchange models in one dimension
• Anomalous long-range correlations at a non-equilibrium phase transition
• Relaxation processes in a system with logarithmic growth
• Diffusion and entanglement in open quantum systems
• Glauber's Ising chain between two thermostats
• Thermodynamic uncertainty relations for many-body systems with fast jump rates and large occupancies
• Lecture notes on large deviations in non-equilibrium diffusive systems
• Systematic analysis of critical exponents in continuous dynamical phase transitions of weak noise theories
• Current fluctuations in the symmetric zero-range process below and at critical density
• Drift of phase fluctuations in the ABC model
• Anomalous current fluctuations and mobility-driven clustering