Abstract
Driving an inertial many-body system out of equilibrium generates complex dynamics due to memory effects and the intricate relationships between the external driving force, internal forces, and transport effects. Understanding the underlying physics is challenging and often requires carrying out case-by-case analysis. To systematically study the interplay between all types of forces that contribute to the dynamics, a method to generate prescribed flow patterns could be of great help. We develop a custom flow method to numerically construct the external force field required to obtain the desired time evolution of an inertial many-body system, as prescribed by its one-body current and density profiles. We validate the custom flow method in a Newtonian system of purely repulsive particles by creating a slow motion dynamics of an out-of-equilibrium process and by prescribing the full time evolution between two distinct equilibrium states. The method can also be used with thermostat algorithms to control the temperature.
Highlights
The precise application of a space- and time-resolved external force field can be used to drive a many-body system out of equilibrium in a controlled way
We construct the timedependent external force required to slow down the observed dynamics by an arbitrarily prescribed factor
Using custom flow to construct the external force that generates the time evolution prescribed in Eq (22) yields the results shown in Fig. 3
Summary
The precise application of a space- and time-resolved external force field can be used to drive a many-body system out of equilibrium in a controlled way. We consider here the inverse problem: to impose the desired dynamics and find the corresponding external field Such inversion, known as a closed-loop control system in control theory [12], is a valuable tool even at the level of individual particles. Using Brownian dynamics simulations, custom flow finds the external force required to generate the desired (imposed) time evolution of both the one-body density and the one-body current distributions. The method is motivated by the exact one-body force balance equation (Sec. II A), and it constructs iteratively the external force field that is required to generate the desired (target) time evolution of both the density and the current distributions (Sec. II B). The method constitutes the solution of a complex inverse problem in statistical physics and implements numerically the map between the kinematic fields (density and current) and the external force field. IV), including one with the Bussi-Donadio-Parrinello thermostat [46]
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