Abstract
Understanding the deep connection of microscopic dynamics and statistical regularity yields insights into the foundation of statistical mechanics. In this work, based on the classical three-body system under the Lennard–Jones potential upon disturbance, we illustrated the elusive non-linear dynamics in terms of the neat frequency-mixing processes, and revealed the emergent statistical regularity in speed distribution along a single particle trajectory. This work demonstrates the promising possibility of classical few-body models for exploring the fundamental questions on the interface of microscopic dynamics and statistical physics.
Graphical abstract
The non-linear dynamics of the perturbed three-body system is analyzed in terms of the neat frequency-mixing processes, and the statistical regularity in the speed distribution along a single particle trajectory is revealed.
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Data availability statement
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.
References
T.Y. Li, J.A. Yorke, Am. Math. Mon. 82(10), 985 (1975)
C. Cercignani et al., Ludwig Boltzmann: the man who trusted atoms (Oxford University Press, Oxford, 1998)
L.P. Kadanoff, From order to chaos II (World Scientific, 1999)
H.S. Dumas, The KAM story (World Scientific Publishing Company, 2014)
N.S. Krylov, Works on the foundations of statistical physics (Princeton University Press, 2014)
C. Neill, P. Roushan, M. Fang, Y. Chen, M. Kolodrubetz, Z. Chen, A. Megrant, R. Barends, B. Campbell, B. Chiaro et al., Nat. Phys. 12(11), 1037 (2016)
I.G. Sinai, Dynamical systems II (Springer, 1989)
R. Zwanzig, Nonequilibrium statistical mechanics (Oxford University Press, 2001)
S.H. Strogatz, Nonlinear dynamics and chaos (CRC Press, 2018)
F. Scheck, Mechanics: from Newton’s laws to deterministic chaos (Springer Science and Business Media, 2010)
B. Yang, J. Pérez-Ríos, F. Robicheaux, Phys. Rev. Lett. 118(15), 154101 (2017)
L. Tonks, Phys. Rev. 50(10), 955 (1936)
Z. Zheng, G. Hu, J. Zhang, Phys. Rev. E 53(4), 3246 (1996)
S. Cox, G. Ackland, Phys. Rev. Lett. 84(11), 2362 (2000)
X. Cao, V.B. Bulchandani, J.E. Moore, Phys. Rev. Lett. 120(16), 164101 (2018)
G.M. Zaslavsky, The physics of chaos in hamiltonian systems (World Scientific, 2007)
J.E. Jones, Proc. R. Soc. Lon. Ser. A 106(738), 463 (1924)
Z. Yao, Soft Matter 13(35), 5905 (2017)
W. Kob, H.C. Andersen, Phys. Rev. E 51(5), 4626 (1995)
N. Xu, M. Wyart, A.J. Liu, S.R. Nagel, Phys. Rev. Lett. 98(17), 175502 (2007)
S. Rützel, S.I. Lee, A. Raman, Proc. R. Soc. Lon. Ser. A 459(2036), 1925 (2003)
H. Fukuda, T. Fujiwara, H. Ozaki, J. Phys. A: Math. Theor. 50(10), 105202 (2017)
A. Rahman, Phys. Rev. 136(2A), A405 (1964)
A.F. Tillack, L.E. Johnson, B.E. Eichinger, B.H. Robinson, J. Chem. Theory Comput. 12(9), 4362 (2016)
P. Bienias, M.J. Gullans, M. Kalinowski, A.N. Craddock, D.P. Ornelas-Huerta, S.L. Rolston, J. Porto, A.V. Gorshkov, Phys. Rev. Lett. 125(9), 093601 (2020)
B. Halperin, D.R. Nelson, Phys. Rev. Lett. 41(2), 121 (1978)
K.J. Strandburg, Rev. Mod. Phys. 60(1), 161 (1988)
N.P. Mitchell, V. Koning, V. Vitelli, W. Irvine, Nat. Mater 16, 89–93 (2017)
Z. Yao, Phys. Rev. E 96(6), 062139 (2017)
H. Hwang, D.A. Weitz, F. Spaepen, Proc. Natl. Acad. Sci. U.S.A. 116(4), 1180 (2019)
T. Vicsek, A. Zafeiris, Phys. Rep. 517(3), 71 (2012)
V. Schaller, A.R. Bausch, Proc. Natl. Acad. Sci. U.S.A. 110(12), 4488 (2013)
N.H. Nguyen, D. Klotsa, M. Engel, S.C. Glotzer, Phys. Rev. Lett. 112(7), 075701 (2014)
Z. Yao, Phys. Rev. Lett. 122(22), 228002 (2019)
E. Fermi, P. Pasta, S. Ulam, M. Tsingou, Studies of the nonlinear problems (Tech. rep, Los Alamos Scientific Lab, 1955)
O. Saporta Katz, E. Efrati, Phys. Rev. Lett. 122, 024102 (2019)
O. Saporta Katz, E. Efrati, Phys. Rev. E 101, 032211 (2020)
J.C. Maxwell, Philos. Mag. 19(124), 19 (1860)
See Supplemental Material for technical details of the numerical approach, and supplemental information about trajectory evolution, frequency spectrum analysis of kinetic energy and statistical analysis of particle trajectories
D. Rapaport, The art of molecular dynamics simulation (Cambridge University Press, Cambridge, 2004)
Z. Yao, Europhys. Lett. 133, 54002 (2021)
D. Sundararajan, The discrete Fourier transform: theory, algorithms and applications (World Scientific, 2001)
E.G. Altmann, A.E. Motter, H. Kantz, Phys. Rev. E 73(2), 026207 (2006)
A.S. Chirkin, A.A. Novikov, G.D. Laptev, J. Opt. B 6(6), S483 (2004)
L.D. Landau, E. Lifshitz, Mechanics, 3rd edn. (Butterworth-Heinemann, Oxford, 1976)
M. Feigenbaum, J. Stat. Phys. 19(1), 25 (1978)
A.S. De Wijn, A. Fasolino, J. Phys. Condens. Matter 21(26), 264002 (2009)
D.G. Saari, Z. Xia, Notices AMS 42(5), 538–546 (1995)
V. Rom-Kedar, D. Turaev, arXiv:2208.14993 (2022)
B. Gaveau, L.S. Schulman, Eur. Phys. J. Spec. Top. 224, 891 (2015)
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grants No. BC4190050).
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Yao, Z. Non-linear dynamics and emergent statistical regularity in classical Lennard–Jones three-body system upon disturbance. Eur. Phys. J. B 96, 159 (2023). https://doi.org/10.1140/epjb/s10051-023-00626-8
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DOI: https://doi.org/10.1140/epjb/s10051-023-00626-8