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 1 st -neighbor atoms. Thus, excess pe fluctuations cannot be due to simple surface effects from the robustly harmonic 1 stneighbor interactions, nor from any details in the simulations or analysis. A simplistic model that includes 2 nd -neighbor interactions matches the excess fluctuations, but only if the 2 nd -neighbor energy is not included in Boltzmann's factor, attributable to anharmonic effects and energy localization. Empirically, adding 2 ndneighbor interactions considerably 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.

Molecular Dynamics Study of Nanoparticles/argon Atoms Size Effects on Atomic Aggregation Phenomena in Ideal Platinum Nanochannel Affected by the External Magnetic Field

“…Numerically, by nanoparticles radius enhancing from 1 nm to 3 nm the aggregation time of these atomic structures decreases from 1.41 ns to 1.29 ns. The classic Navier-Stokes approach are usually used for the simulation of nanofluid flow and heat transfer; however the particle base methods like MD would show better performance at micro and nano scales levels [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59]. Based on present work achievements, we can say the nanoparticle radius variation is an important parameter for using of Ar/Fe3O4 atomic structure in various industrial applications.…”

Multiscale Thermodynamics: Energy, Entropy, and Symmetry from Atoms to Bulk Behavior

“…Thus, the basic requirements of standard statistical mechanics for fast coupling to a homogenous heat reservoir are absent for the primary response in most materials, including liquids, glasses, polymers, and crystals. Moreover, molecular dynamics (MD) simulations of crystals with realistic interactions exhibit excess energy fluctuations that diverge like 1/T as T → 0, deviating from standard statistical mechanics based on − / , but quantitively consistent with energy localization on length scales of nanometers [50]. Nanothermodynamics is necessary to treat independent subsystems that have a distribution of sizes, with realistic particles and heterogeneous interactions, allowing the laws of thermodynamics that govern statistical mechanics to be extended across multiple size scales, down to individual atoms.…”

An Ising Model for Supercooled Liquids and the Glass Transition

“…Other experiments show that glass-forming liquids have a separation of time scales between linear and rotational motion [37,38], suggesting that the two laws conserving momentum may also be uncoupled. Even in idealized single crystals, molecular dynamics simulations show that energy is persistently localized by anharmonic interactions [39], implying that energy localization will be even stronger in disordered systems. In any case, orthogonal dynamics in a simulation does not prohibit correlations between energy change and dipole rotation, it simply separates them so that they may proceed independently on their own preferred time scales.…”

“…Likewise, the London dispersion force that yields realistic van der Waals-like interactions requires quantum effects that involve overlapping wave functions between interacting molecules, and again this coherence is broken by wavefunctions that are localized. Classically, molecular dynamics simulations have shown that, even in idealized single crystals, anharmonic interactions yield significant deviations from standard fluctuation relations due to energy localization [39], which will be much stronger in non-crystalline systems.…”