Transport coefficients from Einstein-Helfand relations using standard and energy-conserving dissipative particle...

Area of Science:

• Mesoscopic physics
• Computational chemistry
• Statistical mechanics

Background:

• Traditional belief questioned the applicability of Einstein-Helfand (EH) formulas to systems with dissipative and random forces.
• Mesoscopic systems, such as Dissipative Particle Dynamics (DPD) and its energy-conserving variant (DPDE), often involve such forces.
• Validating transport coefficient calculations in these systems is crucial for understanding material properties.

Purpose of the Study:

• To demonstrate the validity of standard Einstein-Helfand (EH) formulas for evaluating transport coefficients in mesoscopic systems.
• To verify the applicability of EH formulas to systems incorporating dissipative and random forces.
• To establish the conditions under which EH formulas remain accurate in mesoscopic simulations.

Main Methods:

• Derivation of a mesoscopic heat flux expression specifically for the energy-conserving Dissipative Particle Dynamics (DPDE) method.
• Calculation of thermal conductivity using the derived EH expression.
• Comparison of results obtained from EH formulas with non-equilibrium simulation data.
• Validation across various scenarios, including those with many-body potentials and density/temperature-dependent interactions.

Main Results:

• The standard Einstein-Helfand (EH) formulas are confirmed to be valid for calculating transport coefficients in mesoscopic systems with dissipative and random forces.
• Excellent agreement was observed between EH formula predictions and non-equilibrium simulation results across diverse system configurations.
• The derived mesoscopic heat flux form for DPDE enables accurate thermal conductivity calculations using EH expressions.
• The validity extends to advanced methods like the generalized DPDE (GenDPDE) with complex potentials.

Conclusions:

• Einstein-Helfand (EH) formulas can be reliably employed in equilibrium simulations to determine transport coefficients for mesoscopic systems.
• The key requirements for EH formula validity are the satisfaction of conservation laws and detailed balance conditions.
• The study validates the use of traditional EH formulas for a broader range of mesoscopic systems, including those with complex, state-dependent interactions.