Energy localization and excess fluctuations from long-range interactions in equilibrium molecular dynamics

TL;DR

This study reveals that long-range interactions in molecular dynamics cause significant local energy fluctuations and deviations from expected fluctuation relations, especially in small systems and at low temperatures.

Contribution

It demonstrates the impact of long-range interactions on energy fluctuations and introduces a model accounting for energy localization and mesoscopic effects in equilibrium MD simulations.

Findings

Excess potential energy fluctuations diverge inversely with temperature for long-range interactions.

Energy localization due to anharmonic effects explains deviations from Boltzmann statistics.

Negative energy correlations between neighboring blocks coincide with excess fluctuations.

Abstract

Molecular Dynamics (MD) simulations of standard systems of interacting particles ("atoms") give excellent agreement with the equipartition theorem for the average energy, but we find that these simulations exhibit finite-size effects in the dynamics that cause local fluctuations in energy to deviate significantly from the analogous energy fluctuation relation (EFR). The main conclusion of our study is that systems separated into nanometer-sized "blocks" inside much larger simulations exhibit excess fluctuations in potential energy (pe) that diverge inversely proportional to T in a manner that is strongly dependent on the range of interaction. Specifically, at low T with long-range interactions pe fluctuations exceed the EFR by at least an order of magnitude, dropping abruptly to below the EFR when interactions include only 1st-neighbor atoms. A simplistic model that includes 2nd-neighbor interactions matches the behavior of the excess pe fluctuations, but only if the 2nd-neighbor terms are not included in Boltzmann's factor, attributable to energy localization due to anharmonic effects. Characterizing energy correlations as a function of time and distance reveals that excess pe fluctuations in a block coincide with negative pe correlations between neighboring blocks, whereas reduced pe fluctuations coincide with positive pe correlations. Indeed, anomalous pe fluctuations in small systems at low T can be quantified by using the net energy in Boltzmann's factor that includes the pe from a surrounding shell of similarly small systems, or equivalently an effective local temperature. Our analysis elucidates the source of non-Boltzmann fluctuations, and the need to include mesoscopic thermal effects from the local environment for a consistent theoretical description of the equilibrium fluctuations in MD simulations of standard models with long-range interactions.