Time-Reversible Thermodynamic Irreversibility : One-Dimensional Heat-Conducting Oscillators and Two-Dimensional Newtonian Shockwaves

• Autorzy: Hoover William Graham , Hoover Carol Griswold

Identyfikatory

DOI

:10.12921/cmst.2022.0000022

• Języki publikacji: EN

Abstrakty

EN

We analyze the time-reversible mechanics of two irreversible simulation types. The first is a dissipative onedimensional heat-conducting oscillator exposed to a temperature gradient in a three-dimensional phase space with coordinate q, momentum p, and thermostat control variable ζ. The second type simulates a conservative two-dimensional N-body fluid with 4N phase variables {q, p} undergoing shock compression. Despite the time-reversibility of each of the three oscillator equations and all of the 4N manybody motion equations both types of simulation are irreversible, obeying the Second Law of Thermodynamics. But for different reasons. The irreversible oscillator seeks out an attractive dissipative limit cycle. The likewise irreversible, but thoroughly conservative, Newtonian shockwave eventually generates a reversible near-equilibrium pair of rarefaction fans. Both problem types illustrate interesting features of Lyapunov instability. This instability results in the exponential growth of small perturbations, ∝ e λt where λ is a “Lyapunov exponent”.

Słowa kluczowe

EN

time reversibility; irreversibility; heat conduction; shockwaves; thermodynamics’ Second Law

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2022
• Tom: Vol. 28, No. 4
• Strony: 133--141
• Opis fizyczny: Bibliogr. 12 poz., rys.

Twórcy

autor

Hoover William Graham

• Ruby Valley Research Institute 601 Highway Contract 60 Ruby Valley, Nevada 89833, USA

autor

Hoover Carol Griswold

• Ruby Valley Research Institute 601 Highway Contract 60 Ruby Valley, Nevada 89833, USA

Bibliografia

• [1] S. Nosé, A Unified Formulation of the Constant Temperature Molecular Dynamics Method, The Journal of Chemical Physics 81, 511–519 (1984).
• [2] S. Nosé, A Molecular Dynamics Method for Simulations in the Canonical Ensemble, Molecular Physics 52, 255–268 (1984).
• [3] Wm.G. Hoover, Canonical Dynamics. Equilibrium Phase-Space Distributions, Physical Review A 31, 1695–1697 (1985).
• [4] H.A. Posch, W.G. Hoover, F.J. Vesely, Canonical Dynamics of the Nosé Oscillator: Stability, Order, and Chaos, Physical Review A 33, 4253–4265 (1986).
• [5] H.A. Posch, W.G. Hoover, Time-Reversible Dissipative Attractors in Three and Four Phase-Space Dimensions, Physical Review E 55, 6803–6810 (1997).
• [6] J.C. Sprott, W.G. Hoover, C.G. Hoover, Heat Conduction, and the Lack Thereof, in Time-Reversible Dynamical Systems: Generalized Nosé-Hoover Oscillators with a Temperature Gradient, Physical Review E 89, 042914 (2014).
• [7] W.G. Hoover, H.A. Posch, B.L. Holian, M.J. Gillan, M. Mareschal, C. Massobrio, Dissipative Irreversibility from Nosé’s Reversible Mechanics, Molecular Simulation 1, 79–86 (1987).
• [8] B.L. Holian, W.G. Hoover, H.A. Posch, Resolution of Loschmidt’s Paradox: The Origin of Irreversible Behavior in Reversible Atomistic Dynamics, Physical Review Letters 59, 10–13 (1987).
• [9] W.G. Hoover, C.G. Hoover, Time-Symmetry Breaking in Hamiltonian Mechanics. Part II. A Memoir for Berni Julian Alder [1925–2020], Computational Methods in Science and Technology 26, 101–110 (2020).
• [10] W.G. Hoover, C.G. Hoover, Time-Symmetry Breaking in Hamiltonian Mechanics. Part III. A Memoir for Douglas James Henderson [1934–2020], Computational Methods in Science and Technology 26, 111–120 (2020).
• [11] J.C. Sprott, W.G. Hoover, C.G. Hoover, Elegant Simulations, World Scientific, Singapore (2023).
• [12] M. Ross, B.J. Alder, Shock Compression of Argon II. Nonadditive Repulsive Potential, The Journal of Chemical Physics 46, 4203–4210 (1967).

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).