Exact Fluctuations of Nonequilibrium Steady States from Approximate Auxiliary Dynamics

This paper was published in Physical Review Letters -- the most prestigious journal of the American Physical Society. It details a simulation technique that can be used to efficiently sample nonequilibrium steady states. Our idea was to exploit a connection with quantum mechanics to construct approximate guiding distribution functions (GDFs) to calculate properties of nonequilibrium steady states following the framework of Large Deviation Theory (LDT).

Nonequilbrium physics arise generally in driven systems. The distribution of configurations (here they are essentially trajectories) that entail such systems are remarkably different from those that can be represented via equilibrium statistical mechanics (aka Boltzmann distribution). This makes calculation of such properties very challenging. LDT provides an unifying framework that lends remarkable insight into such processes. However, there are technical issues with such calculations leading to exponentially growing variance in Monte-Carlo estimators. While there is no way to eliminate this problem for any realistic system, our technique allows it to be mitigated in practical terms. In fact, our work outlines a framework via which systematically improvable GDFs may be constructed. Each level of added sophistication leads to improvement of efficiency in the calculations, sometimes by orders of magnitudes.

The figure illustrates the power of our technique. The left image shows the nonequilibrium "free energy" for different "temperatures" for the Symmetric Simple Exclusion Process (SSEP). (Note that these are not actually free-energies or temperature since they are equilibrium ideas.) The inset shows the improvement of efficiency as the level of GDF is improved (green to cyan). Relative to the blue curve, we obtain about 40 times increase in sampling efficiency. The right image uses a cluster mean-field to calculate GDFs that are used to sample a 2D Weakly ASEP process and compute the susceptibilities. This is a remarkable system exhibiting a dynamical phase transition starting with an uniform density state to a traveling wave state as the effective "temperature" is reduced. At the critical point the system exhibits long range dynamical correlations leading to a peaking of the susceptibility.