What is liquid? Lyapunov instability reveals symmetry-breaking irreversibilities hidden within Hamilton's many-body equations of motion
Typical Hamiltonian liquids display exponential "Lyapunov instability", also called "sensitive dependence on initial conditions". Although Hamilton's equations are thoroughly time-reversible, the forward and backward Lyapunov instabilities can differ, qualitatively. In numer...
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| Дата: | 2015 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут фізики конденсованих систем НАН України
2015
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/153582 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | What is liquid? Lyapunov instability reveals symmetry-breaking irreversibilities hidden within Hamilton's many-body equations of motion / Wm.G. Hoover, C.G. Hoover // Condensed Matter Physics. — 2015. — Т. 18, № 1. — С. 13003:1-13. — Бібліогр.: 22 назв. — англ. |
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irk-123456789-1535822019-06-15T01:29:57Z What is liquid? Lyapunov instability reveals symmetry-breaking irreversibilities hidden within Hamilton's many-body equations of motion Hoover, Wm.G. Hoover, C.G. Typical Hamiltonian liquids display exponential "Lyapunov instability", also called "sensitive dependence on initial conditions". Although Hamilton's equations are thoroughly time-reversible, the forward and backward Lyapunov instabilities can differ, qualitatively. In numerical work, the expected forward/backward pairing of Lyapunov exponents is also occasionally violated. To illustrate, we consider many-body inelastic collisions in two space dimensions. Two mirror-image colliding crystallites can either bounce, or not, giving rise to a single liquid drop, or to several smaller droplets, depending upon the initial kinetic energy and the interparticle forces. The difference between the forward and backward evolutionary instabilities of these problems can be correlated with dissipation and with the Second Law of Thermodynamics. Accordingly, these asymmetric stabilities of Hamilton's equations can provide an "Arrow of Time". We illustrate these facts for two small crystallites colliding so as to make a warm liquid. We use a specially-symmetrized form of Levesque and Verlet's bit-reversible Leapfrog integrator. We analyze trajectories over millions of collisions with several equally-spaced time reversals. 2015 Article What is liquid? Lyapunov instability reveals symmetry-breaking irreversibilities hidden within Hamilton's many-body equations of motion / Wm.G. Hoover, C.G. Hoover // Condensed Matter Physics. — 2015. — Т. 18, № 1. — С. 13003:1-13. — Бібліогр.: 22 назв. — англ. 1607-324X DOI:10.5488/CMP.18.13003 arXiv:1405.2485 PACS: 05.10.-a, 05.45.-a http://dspace.nbuv.gov.ua/handle/123456789/153582 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Typical Hamiltonian liquids display exponential "Lyapunov instability", also called "sensitive dependence on initial conditions". Although Hamilton's equations are thoroughly time-reversible, the forward and backward Lyapunov instabilities can differ, qualitatively. In numerical work, the expected forward/backward pairing of Lyapunov exponents is also occasionally violated. To illustrate, we consider many-body inelastic collisions in two space dimensions. Two mirror-image colliding crystallites can either bounce, or not, giving rise to a single liquid drop, or to several smaller droplets, depending upon the initial kinetic energy and the interparticle forces. The difference between the forward and backward evolutionary instabilities of these problems can be correlated with dissipation and with the Second Law of Thermodynamics. Accordingly, these asymmetric stabilities of Hamilton's equations can provide an "Arrow of Time". We illustrate these facts for two small crystallites colliding so as to make a warm liquid. We use a specially-symmetrized form of Levesque and Verlet's bit-reversible Leapfrog integrator. We analyze trajectories over millions of collisions with several equally-spaced time reversals. |
| format |
Article |
| author |
Hoover, Wm.G. Hoover, C.G. |
| spellingShingle |
Hoover, Wm.G. Hoover, C.G. What is liquid? Lyapunov instability reveals symmetry-breaking irreversibilities hidden within Hamilton's many-body equations of motion Condensed Matter Physics |
| author_facet |
Hoover, Wm.G. Hoover, C.G. |
| author_sort |
Hoover, Wm.G. |
| title |
What is liquid? Lyapunov instability reveals symmetry-breaking irreversibilities hidden within Hamilton's many-body equations of motion |
| title_short |
What is liquid? Lyapunov instability reveals symmetry-breaking irreversibilities hidden within Hamilton's many-body equations of motion |
| title_full |
What is liquid? Lyapunov instability reveals symmetry-breaking irreversibilities hidden within Hamilton's many-body equations of motion |
| title_fullStr |
What is liquid? Lyapunov instability reveals symmetry-breaking irreversibilities hidden within Hamilton's many-body equations of motion |
| title_full_unstemmed |
What is liquid? Lyapunov instability reveals symmetry-breaking irreversibilities hidden within Hamilton's many-body equations of motion |
| title_sort |
what is liquid? lyapunov instability reveals symmetry-breaking irreversibilities hidden within hamilton's many-body equations of motion |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/153582 |
| citation_txt |
What is liquid? Lyapunov instability reveals symmetry-breaking irreversibilities hidden within Hamilton's many-body equations of motion / Wm.G. Hoover, C.G. Hoover // Condensed Matter Physics. — 2015. — Т. 18, № 1. — С. 13003:1-13. — Бібліогр.: 22 назв. — англ. |
| series |
Condensed Matter Physics |
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2023-05-20T17:41:47Z |
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