Deterministic chaos and
nonequilibrium statistical mechanics:
outline of contents
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0.
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Introduction
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list of references
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table of contents
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overview: models and key ideas
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1.
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Basic concepts of dynamical systems theory
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deterministic chaos in piecewise linear maps
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Lyapunov exponents, dynamical entropies, and fractal dimensions
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probability measures and the Frobenius-Perron equation
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2.
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Chaotic diffusion
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random walks
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diffusion equation and escape rate formalism
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Green-Kubo formula and fractal functions
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thermodynamic formalism
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cycle expansion methods
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anomalous diffusion
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3.
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Chaotic currents and chaotic reaction-diffusion
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linear and nonlinear response in simple biased maps
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Langevin equations, ratchets, and molecular motors
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reaction-diffusion systems
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4.
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Disordered dynamical systems
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quenched disorder and subdiffusion
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diffusion on disordered lattices
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chaotic diffusion and noise
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5.
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Chaotic transport in multibaker maps
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ergodic properties, dynamical systems classifications, and time-reversibility
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relation between one-dimensional maps and baker maps
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diffusive multibaker maps
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biased multibaker maps and entropy production
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6.
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Chaotic diffusion in the periodic Lorentz gas
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definition of the model and dynamical properties
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relation between the periodic Lorentz gas and two-dimensional maps
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analysis of the density-dependent diffusion coefficient
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Boltzmann equation, kinetic theory, and Lyapunov exponents
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7.
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the thermostated systems approach to nonequilibrium steady states
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the Gaussian thermostated Lorentz gas
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chaotic and fractal properties of nonequilibrium steady states in thermostated
systems
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the Nose-Hoover thermostat, generalized Liouville equation, and generalized
Hamiltonian formalism
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criticism of this approach
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8.
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the thermostated systems approach revisited
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non-ideal Gaussian and Nose-Hoover thermostats
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stochastic boundary conditions
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thermostating by deterministic scattering
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do there exist universal chaotic and fractal properties of thermostated
nonequilibrium steady states?
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deterministic thermostats, active Brownian particles, and cell motility
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9.
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fluctuation theorems
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10.
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-entropies
and microscopic chaos in experiments?