Stochastic Norton Dynamics: An Alternative Approach for the Computation of Transport Coefficients in Dissipative Particle Dynamics

Abstract: We study a novel alternative approach for the computation of transport coefficients at mesoscales. While standard nonequilibrium molecular dynamics (NEMD) approaches fix the forcing and measure the average induced flux in the system driven out of equilibrium, the so-called ``stochastic Norton dynamics'' instead fixes the value of the flux and measures the average magnitude of the forcing needed to induce it. We extend recent results obtained in Langevin dynamics to consider the generalisation of the stochastic Norton dynamics in the popular dissipative particle dynamics (DPD) at mesoscales, important for a wide range of complex fluids and soft matter applications. We demonstrate that the responses profiles for both the NEMD and stochastic Norton dynamics approaches coincide in both linear and nonlinear regimes, indicating that the stochastic Norton dynamics can indeed act as an alternative approach for the computation of transport coefficients, including the mobility and the shear viscosity, as the NEMD dynamics. In addition, based on the linear response of the DPD system with small perturbations, we derive a closed-form expression for the shear viscosity, and numerically validate its effectiveness with various types of external forces. Moreover, our numerical experiments demonstrate that the stochastic Norton dynamics approach clearly outperforms the NEMD dynamics in controlling the asymptotic variance, a key metric to measure the associated computational costs, particularly in the high friction limit.