Additivity of the Excess Energy Dissipation Rate in a Dynamically Self-Assembled System

Despite its prevalence in biological systems and its promise as a route to adaptive and/or self-healing materials, dynamic self-assembly (DySA) far from thermodynamic equilibrium remains poorly understood. In this context, it is desirable to develop general thermodynamic relations describing the steady-state configurations of such dissipative assemblies. Here, numerical simulations and analytical methods are used to calculate the viscous energy dissipation rates in a prototypical, magnetohydrodynamic DySA system. In addition to the well-established criteria of mechanical equilibrium, it is shown that the naturally forming steady-state configurations/flows are characterized by a fundamentally different relation based on the viscous energy dissipation. Specifically, the total dissipation of the n-particle system may be expressed as a sum of pairwise interactions derived from the analogous two-particle system. This dissipation additivity holds despite the presence of many-body forces/torques between the particles and may prove useful in estimating the viscosities of colloidal suspensions.