Mapping Nonequilibrium onto Equilibrium: The Macroscopic Fluctuations of Simple Transport Models

We study a simple transport model driven out of equilibrium by reservoirs at the boundaries, corresponding to the hydrodynamic limit of the symmetric simple exclusion process. We show that a nonlocal transformation of densities and currents maps the large deviations of the model into those of an open, isolated chain satisfying detailed balance, where rare fluctuations are the time reversals of relaxations. We argue that the existence of such a mapping is the immediate reason why it is possible for this model to obtain an explicit solution for the large-deviation function of densities through elementary changes of variables. This approach can be generalized to the other models previously treated with the macroscopic fluctuation theory.

💡 Research Summary

The paper tackles one of the most challenging problems in nonequilibrium statistical mechanics: obtaining an explicit expression for the large‑deviation functional (LDF) of a driven diffusive system. The authors focus on the one‑dimensional symmetric simple exclusion process (SSEP) in the hydrodynamic limit, where particles hop on a lattice with at most one particle per site and are coupled to two reservoirs at the boundaries that impose different chemical potentials. In this setting the system settles into a nonequilibrium steady state (NESS) characterized by a non‑uniform density profile and a constant particle current.

Within the macroscopic fluctuation theory (MFT) the probability of observing a space‑time trajectory ((\rho(x,t),J(x,t))) obeys a large‑deviation principle (P\sim\exp