The dependence between forces and dissipation rates mediating dynamic self-assembly

Dynamic self-assembly (DySA) outside of thermodynamic equilibrium underlies many forms of adaptive and intelligent behaviors in both natural and artificial systems. At the same time, the fundamental principles governing DySA systems remain largely undeveloped. In this context, it is desirable to relate the forces mediating self-assembly to the nonequilibrium thermodynamics of the system -specifically, to the rate of energy dissipation. In this paper, numerical simulations are used to calculate dissipation rates in a prototypical, magneto-hydrodynamic DySA system, and to relate these rates to dissipative forces acting between the system's components. It is found that (i) dissipative forces are directly proportional to the gradient of the dissipation rate with respect to a coordinate characterizing the steady-state assemblies, and (ii) the constant of proportionality linking these quantities is a characteristic time describing the response of the system to small, externally applied perturbations. This relationship complements and extends the applicability of Prigogine's minimal-entropy-production formalism.