Issue 17, 2023

Transport coefficients from Einstein–Helfand relations using standard and energy-conserving dissipative particle dynamics methods

Abstract

In this article we demonstrate that contrary to general belief, the standard Einstein–Helfand (EH) formulas are valid for the evaluation of transport coefficients of systems containing dissipative and random forces provided that for these mesoscopic systems: (i) the corresponding conservation laws are satisfied, and (ii) the transition probabilities satisfy detailed balance. Dissipative particle dynamics (DPD) and energy-conserving DPD methods (DPDE), for instance, are archetypical of such mesoscopic approaches satisfying these properties. To verify this statement, we have derived a mesoscopic heat flux form for the DPDE method, suitable for the calculation of the thermal conductivity from an EH expression. We have compared EH measurements against non-equilibrium simulation values for different scenarios, including many-body potentials, and have found excellent agreement in all cases. The expressions are valid notably for systems with density- and temperature-dependent potentials, such as the recently developed generalised DPDE method (GenDPDE) [Avalos et al., Phys. Chem. Chem. Phys., 2019, 21, 24891]. We thus demonstrate that traditional EH formulas in equilibrium simulations can be widely used to obtain transport coefficients, provided that the appropriate expression for the associated flux is used.

Graphical abstract: Transport coefficients from Einstein–Helfand relations using standard and energy-conserving dissipative particle dynamics methods

Article information

Article type
Paper
Submitted
16 Oct 2022
Accepted
24 Mar 2023
First published
06 Apr 2023
This article is Open Access
Creative Commons BY-NC license

Phys. Chem. Chem. Phys., 2023,25, 12025-12040

Transport coefficients from Einstein–Helfand relations using standard and energy-conserving dissipative particle dynamics methods

D. C. Malaspina, M. Lísal, J. P. Larentzos, J. K. Brennan, A. D. Mackie and J. B. Avalos, Phys. Chem. Chem. Phys., 2023, 25, 12025 DOI: 10.1039/D2CP04838H

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