Microscopic derivation of coarse-grained, energy-conserving generalized Langevin dynamics

Area of Science:

• Computational physics
• Statistical mechanics
• Condensed matter theory

Background:

• Simulating nonequilibrium phenomena like thermal transport requires internal energy conservation.
• Coarse-grained generalized Langevin equation (CG GLE) dynamics face challenges with dissipative interactions.
• Existing energy-conserving extensions, like DPD-E, have limitations.

Purpose of the Study:

• To rigorously derive energy-conserving variants of CG GLE dynamics from microscopic principles.
• To extend CG GLE to handle nonequilibrium conditions necessary for studying phenomena like heat transport.
• To provide a general formalism for CG simulations of various observables and ensembles.

Main Methods:

• Utilized the Mori-Zwanzig projection operator method in the Heisenberg picture.
• Applied a recent interpretation of the Zwanzig projection operator for exact term calculation.
• Extended the formalism to quasiequilibrium conditions using the generalized canonical ensemble and nonequilibrium statistical operator (NSO) method.

Main Results:

• Derived two energy-conserving CG GLE variants for internal energy observables.
• Obtained closed microscopic expressions for conductive heat transfer coefficients.
• Identified additional energy transfer terms compared to existing DPD-E models.
• Revealed a fluctuation-dissipation-like relation between heat transfer coefficients and random forces.

Conclusions:

• The derived energy-conserving CG GLE dynamics provide a more accurate framework for simulating nonequilibrium phenomena.
• The method offers a rigorous foundation for extending CG simulations to complex systems and ensembles.
• The findings advance the development of computational tools for condensed matter physics research.