Universal anomalous fluctuations in charged single-file systems

Introducing a general class of one-dimensional single-file systems (meaning that particle crossings are prohibited) of interacting hardcore particles with internal degrees of freedom (called charge), we exhibit a novel type of dynamical universality reflected in anomalous statistical properties of macroscopic fluctuating observables such as charge transfer. We find that stringent dynamical constraints lead to universal anomalous statistics of cumulative charge currents manifested both on the timescale characteristic of typical fluctuations and also in the rate function describing rare events. By computing the full counting statistics of net transferred charge between two extended subsystems, we establish a number of unorthodox dynamical properties in an analytic fashion. Most prominently, typical fluctuations in equilibrium are governed by a universal distribution that markedly deviates from the expected Gaussian statistics, whereas large fluctuations are described by an exotic large-deviation rate function featuring an exceptional triple critical point. Far from equilibrium, competition between dynamical phases leads to dynamical phase transitions of first and second order and spontaneous breaking of fluctuation symmetry of the univariate charge large-deviation function. The rich phenomenology of the outlined dynamical universality is exemplified on an exactly solvable classical cellular automaton of charged hardcore particles. We determine the dynamical phase diagram in the framework of Lee-Yang's theory of phase transitions and exhibit a hyper-dimensional diagram of distinct dynamical regimes. Our findings lead us to conclude that the conventional classification of dynamical universality classes based on the algebraic dynamical exponents and asymptotic scaling functions that characterize hydrodynamic relaxation of the dynamical structure factor is incomplete and calls for refinement.