Probing fluctuating hydrodynamics through current fluctuations in hard rod gas

Abstract

We study the full counting statistics of the integrated current in a one-dimensional hard-rod gas in equilibrium, employing two recently proposed fluctuating hydrodynamic frameworks: (i) Ballistic Macroscopic Fluctuation Theory (BMFT) and (ii) diffusive fluctuating hydrodynamic theory based on correlated Brownian motion approximation of hard-rod quasiparticles (CBFHD). We investigate how the predictions of these two approaches compare with each other and with the underlying microscopic dynamics. We show within BMFT that the current distribution admits a large-deviation form under ballistic scaling, and we derive an explicit expression for the large-deviation function, valid for an arbitrary inhomogeneous initial state factorized in point-particle coordinates. The corresponding current cumulants are also obtained. We subsequently analyze the current statistics within the CBFHD framework, which explicitly incorporates stochastic noise and dissipative terms, and demonstrate that the current distribution likewise obeys a large-deviation principle in this approach. We find that, while BMFT predictions for the first few cumulants and the rate function are in excellent agreement with direct numerical simulations of the microscopic hard-rod dynamics, CBFHD prediction is not. We further verify the predictions of the CBFHD independently using a collection of correlated Brownian motions, which provides an approximate description of the dynamics of hard-rod quasiparticles. Our findings indicate that CBFHD does not accurately capture large-scale current fluctuations in the hard-rod gas, whereas BMFT yields predictions in quantitative agreement with the microscopic dynamics, at least in the context of full counting statistics.