Energy localization and excess fluctuations from long-range interactions in equilibrium molecular dynamics
arXiv:1904.00544 · doi:10.1016/j.physa.2019.123228
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.
arXiv comment29 pages, 6 figures
References in corpus (21)
- A nonequilibrium equality for free energy differences
- Stochastic thermodynamics, fluctuation theorems, and molecular machines
- The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
- Dynamical Ensembles in Nonequilibrium Statistical Mechanics
- Multicanonical Ensemble: A New Approach to Simulate First-order Phase Transitions
- A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
- Fluctuation-Dissipation: Response Theory in Statistical Physics
- Dissipation: The phase-space perspective
- The Fermi-Pasta-Ulam problem: 50 years of progress
- Observation of multifractality in Anderson localization of ultrasound
- Intermittent many-body dynamics at equilibrium
- Thermodynamic theory of equilibrium fluctuations
- The Big World of Nanothermodynamics
- Temperature fluctuations in canonical systems: Insights from molecular dynamics simulations
- Applications of the Generalised Langevin Equation: towards a realistic description of the baths
- Ring statistics in 2D-silica: effective temperatures in equilibrium
- Beyond the Boltzmann factor for corrections to scaling in ferromagnetic materials and critical fluids
- Localization-delocalization transition for disordered cubic harmonic lattices
- Fluctuation-theory constraint for extensive entropy in Monte-Carlo simulations
- 1/f Noise from the Laws of Thermodynamics for Finite-Size Fluctuations
- Fluctuation theorems and 1/f noise from a simple matrix