najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2025-16-4-407-418najo-1431Research ArticlePHYSICSФИЗИКАInherent noise present in molecular dynamics simulations and what can be learnt from it for 2D Lennard–Jones systemСобственный шум, присутствующий в моделировании методом молекулярной динамики, и то, что можно извлечь из него для двумерной системы Леннарда-Джонсаhttps://orcid.org/0000-0001-5978-4530КондринМ. В.KondrinM. V.

Михаил Владиславович Кондрин

Mikhail V. Kondrin

108840 Troitsk, Moscow, Russia

mkondrin@hppi.troitsk.ruЛебедьЮ. Б.LebedYu. B.

Юлия Борисовна Лебедь

Yulia B. Lebed

117312 Moscow, Russia

jlebed@inr.ruInstitute for High Pressure Physics RASRussian FederationInstitute for Nuclear Research RASRussian Federation202503092025164407418Copyright © Kondrin M.V., Lebed Y.B., 20252025Кондрин М.В., Лебедь Ю.Б.Kondrin M.V., Lebed Y.B.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1431

We have investigated the influence of finite number of particles used in molecular dynamics simulations on the fluctuations of thermodynamic properties. As a case study, the two-dimensional Lennard–Jones system was used. The 2D Lennard–Jones is an archetypal system and a subject of long debate about whether it has continuous (infinite-order) or discontinuous (the first-order) melting transition. We have found, that anomalies on the equation of state (the van-der-Waals or Myer–Wood loops), previously considered a hallmark of the first order phase transition, are at best at the level of noise, since their magnitude is the same as the amplitude of pressure fluctuations. So, they could be regarded as a statistically unsignificant effect. Also, we estimated inherent statistical noise present in computer simulations, and came to the conclusion, that it is larger than predicted by statistical physics, and the difference between them (called algorithmic fluctuations) may be due to the computer-related issues.

Мы исследовали влияние конечного числа частиц, используемых при моделировании  методом молекулярной динамики, на флуктуации термодинамических свойств. В качестве примера была использована двумерная система Леннарда-Джонса. Двумерная система Леннарда-Джонса - это архетипическая система и предмет долгих споров о том, имеет ли она непрерывный (бесконечного порядка) или переход  первого рода в точке плавления. Мы обнаружили, что аномалии в  уравнении состояния (петли Ван-дер-Ваальса или Майера-Вуда), которые ранее считались отличительной чертой фазового перехода первого рода, в лучшем случае находятся на уровне шума, поскольку их величина  совпадает с амплитудой флуктуаций давления. Таким образом, их можно рассматривать как статистически незначительный эффект. Кроме того, мы оценили характерный статистический шум, присутствующий в компьютерном моделировании, и пришли к выводу, что он больше, чем предсказывает статистическая физика, и разница между ними  (называемая алгоритмическими флуктуациями) может быть вызвана  проблемами, связанными с компьютерной реализацией вычислений.

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The authors declare that there are no conflicts of interest present.