Chaos and irreversibility in simple model systems.

The multifractal link between chaotic time-reversible mechanics and thermodynamic irreversibility is illustrated for three simple chaotic model systems: the Baker Map, the Galton Board, and many-body color conductivity. By scaling time, or the momenta, or the driving forces, it can be shown that the dissipative nature of the three thermostated model systems has analogs in conservative Hamiltonian and Lagrangian mechanics. Links between the microscopic nonequilibrium Lyapunov spectra and macroscopic thermodynamic dissipation are also pointed out. (c) 1998 American Institute of Physics.

[1]  Multifractals from Hamiltonian many-body molecular dynamics , 1997 .

[2]  W. G. Hoover.  Computational Statistical Mechanics , 1991 .

[3]  Hoover,et al.  Phase-space singularities in atomistic planar diffusive flow. , 1989, Physical review. A, General physics.

[4]  William G. Hoover,et al.  Shock-wave structure via nonequilibrium molecular dynamics and Navier-Stokes continuum mechanics , 1980 .

[5]  H. Posch,et al.  Negative Lyapunov exponents for dissipative systems , 1988 .

[7]  P. Gaspard,et al.  Fick's law and fractality of nonequilibrium stationary states in a reversible multibaker map , 1995 .

[8]  L. Verlet,et al.  Molecular dynamics and time reversibility , 1993 .

[9]  William G. Hoover,et al.  Lorentz gas shear viscosity via nonequilibrium molecular dynamics and Boltzmann's equation , 1985 .

[10]  P. Gaspard.  Entropy production in open volume-preserving systems , 1997 .

[11]  W. Hoover,et al.  Argon Shear Viscosity via a Lennard-Jones Potential with Equilibrium and Nonequilibrium Molecular Dynamics , 1973 .

[12]  Wolfgang Breymann,et al.  Institute for Mathematical Physics Equivalence of Irreversible Entropy Production in Driven Systems: an Elementary Chaotic Map Approach , 2009 .

[13]  B. Moran,et al.  Viscous attractor for the Galton board. , 1992, Chaos.

[14]  C. G. Hoover,et al.  Irreversibility in the Galton board via conservative classical and quantum hamiltonian and gaussian dynamics , 1988 .

[15]  Vollmer,et al.  Entropy Production for Open Dynamical Systems. , 1996, Physical review letters.

[16]  H. Posch,et al.  Large-system hydrodynamic limit for color conductivity in two dimensions , 1998 .

[17]  Lebowitz,et al.  Derivation of Ohm's law in a deterministic mechanical model. , 1993, Physical review letters.

[18]  L. Andrey.  Note concerning the paper “the rate of entropy change in non-hamiltonian systems” , 1986 .

[19]  William G. Hoover,et al.  Diffusion in a periodic Lorentz gas , 1987 .

[20]  Lebowitz,et al.  Stationary shear flow in boundary driven Hamiltonian systems. , 1995, Physical review letters.

[21]  Michel Mareschal,et al.  Microscopic simulations of complex flows , 1990 .

[22]  G. Morriss,et al.  Hamiltonian formulation of the Gaussian isokinetic thermostat. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[23]  Hoover,et al.  Time-reversible dissipative ergodic maps. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  S. Edwards,et al.  The computer study of transport processes under extreme conditions , 1972 .

[25]  H. Posch,et al.  Resolution of Loschmidt's paradox: The origin of irreversible behavior in reversible atomistic dynamics. , 1987, Physical review letters.

[26]  Michel Mareschal,et al.  Microscopic simulations of complex hydrodynamic phenomena , 1993 .

[27]  J. Yorke,et al.  Dimension of chaotic attractors , 1982 .

[28]  Carl P. Dettmann,et al.  Hamiltonian reformulation and pairing of Lyapunov exponents for Nose-Hoover dynamics , 1996, chao-dyn/9612018.

[29]  Grégoire Nicolis,et al.  Nonequilibrium thermodynamics of dynamical systems , 1996 .

[30]  Wolfgang Breymann,et al.  Transient chaos: the origin of transport in driven systems , 1996 .

[31]  Hoover,et al.  Comment I on "Possible experiment to check the reality of a nonequilibrium temperature" , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[32]  K. Pearson,et al.  The Life, Letters and Labours of Francis Galton , 1931, Nature.

[33]  G. Nicolis,et al.  Transport properties, Lyapunov exponents, and entropy per unit time. , 1990, Physical review letters.

[34]  William G. Hoover,et al.  Dissipative Irreversibility from Nosé's Reversible Mechanics , 1987 .

[35]  Evans,et al.  Probability of second law violations in shearing steady states. , 1993, Physical review letters.

[36]  W. Fleischhacker,et al.  Pioneering ideas for the physical and chemical sciences : Josef Loschmidt's contributions and modern developments in structural organic chemistry, atomistics, and statistical mechanics : proceedings of the Joseph Loschmidt Symposium, held June 25-27, 1995, in Vienna, Austria , 1997 .

[37]  J. Clarke,et al.  Investigation of the homogeneous-shear nonequilibrium-molecular-dynamics method. , 1992, Physical review. A, Atomic, molecular, and optical physics.