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

Ralph V. Chamberlin, Vladimiro Mujica, Sergei Izvekov, James P. Larentzos

Research output: Contribution to journalArticle

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). We have made a detailed analysis of Lennard-Jones atoms to track the origin of such unphysical fluctuations, which must be corrected for an appropriate description of the statistical mechanics of small systems, especially at low temperatures (T). Similar behavior is found in a model of nitromethane at higher T. 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. Thus, excess pe fluctuations cannot be due to simple surface effects from the robustly harmonic 1st-neighbor interactions, nor from any details in the simulations or analysis. A simplistic model that includes 2nd-neighbor interactions matches the excess fluctuations, but only if the 2nd-neighbor energy is not included in Boltzmann's factor, attributable to anharmonic effects and energy localization. Empirically, adding 2nd-neighbor interactions greatly increases the width of the pe distribution, suggesting that Anderson localization may play a role. Characterizing energy correlations as a function of time and distance reveals that excess pe fluctuations in each 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 can be quantified using a net local energy in Boltzmann's factor that includes pe from the surrounding shell of similarly small systems, or equivalently an effective local temperature. Our results and analysis elucidate 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.

Original languageEnglish (US)
Article number123228
JournalPhysica A: Statistical Mechanics and its Applications
DOIs
StateAccepted/In press - Jan 1 2019

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Long-range Interactions
Molecular Dynamics
Excess
Fluctuations
molecular dynamics
potential energy
Energy
interactions
energy
simulation
Interaction
Ludwig Boltzmann
Molecular Dynamics Simulation
equipartition theorem
atoms
nitromethane
Anderson Localization
Surface Effects
Equipartition
statistical mechanics

Keywords

  • Fluctuations
  • Localization
  • MD simulations
  • Nanoscale dynamics
  • Specific heat
  • Statistical physics

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics

Cite this

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title = "Energy localization and excess fluctuations from long-range interactions in equilibrium molecular dynamics",
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). We have made a detailed analysis of Lennard-Jones atoms to track the origin of such unphysical fluctuations, which must be corrected for an appropriate description of the statistical mechanics of small systems, especially at low temperatures (T). Similar behavior is found in a model of nitromethane at higher T. 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. Thus, excess pe fluctuations cannot be due to simple surface effects from the robustly harmonic 1st-neighbor interactions, nor from any details in the simulations or analysis. A simplistic model that includes 2nd-neighbor interactions matches the excess fluctuations, but only if the 2nd-neighbor energy is not included in Boltzmann's factor, attributable to anharmonic effects and energy localization. Empirically, adding 2nd-neighbor interactions greatly increases the width of the pe distribution, suggesting that Anderson localization may play a role. Characterizing energy correlations as a function of time and distance reveals that excess pe fluctuations in each 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 can be quantified using a net local energy in Boltzmann's factor that includes pe from the surrounding shell of similarly small systems, or equivalently an effective local temperature. Our results and analysis elucidate 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.",
keywords = "Fluctuations, Localization, MD simulations, Nanoscale dynamics, Specific heat, Statistical physics",
author = "Chamberlin, {Ralph V.} and Vladimiro Mujica and Sergei Izvekov and Larentzos, {James P.}",
year = "2019",
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doi = "10.1016/j.physa.2019.123228",
language = "English (US)",
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TY - JOUR

T1 - Energy localization and excess fluctuations from long-range interactions in equilibrium molecular dynamics

AU - Chamberlin, Ralph V.

AU - Mujica, Vladimiro

AU - Izvekov, Sergei

AU - Larentzos, James P.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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). We have made a detailed analysis of Lennard-Jones atoms to track the origin of such unphysical fluctuations, which must be corrected for an appropriate description of the statistical mechanics of small systems, especially at low temperatures (T). Similar behavior is found in a model of nitromethane at higher T. 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. Thus, excess pe fluctuations cannot be due to simple surface effects from the robustly harmonic 1st-neighbor interactions, nor from any details in the simulations or analysis. A simplistic model that includes 2nd-neighbor interactions matches the excess fluctuations, but only if the 2nd-neighbor energy is not included in Boltzmann's factor, attributable to anharmonic effects and energy localization. Empirically, adding 2nd-neighbor interactions greatly increases the width of the pe distribution, suggesting that Anderson localization may play a role. Characterizing energy correlations as a function of time and distance reveals that excess pe fluctuations in each 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 can be quantified using a net local energy in Boltzmann's factor that includes pe from the surrounding shell of similarly small systems, or equivalently an effective local temperature. Our results and analysis elucidate 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.

AB - 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). We have made a detailed analysis of Lennard-Jones atoms to track the origin of such unphysical fluctuations, which must be corrected for an appropriate description of the statistical mechanics of small systems, especially at low temperatures (T). Similar behavior is found in a model of nitromethane at higher T. 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. Thus, excess pe fluctuations cannot be due to simple surface effects from the robustly harmonic 1st-neighbor interactions, nor from any details in the simulations or analysis. A simplistic model that includes 2nd-neighbor interactions matches the excess fluctuations, but only if the 2nd-neighbor energy is not included in Boltzmann's factor, attributable to anharmonic effects and energy localization. Empirically, adding 2nd-neighbor interactions greatly increases the width of the pe distribution, suggesting that Anderson localization may play a role. Characterizing energy correlations as a function of time and distance reveals that excess pe fluctuations in each 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 can be quantified using a net local energy in Boltzmann's factor that includes pe from the surrounding shell of similarly small systems, or equivalently an effective local temperature. Our results and analysis elucidate 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.

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KW - Nanoscale dynamics

KW - Specific heat

KW - Statistical physics

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