Contents -- Preface -- 1. Introduction and outline -- 1.1 Hamiltonian dynamical systems approach to nonequilibrium statistical mechanics -- 1.2 Thermostated dynamical systems approach to nonequilibrium statistical mechanics -- 1.3 The red thread through this book -- Part 1: Fractal transport coefficients -- 2. Deterministic diffusion -- 2.1 A simple model for deterministic diffusion -- 2.2 A parameter-dependent fractal diffusion coefficient -- 2.3 Summary -- 3. Deterministic drift-diffusion -- 3.1 Drift-diffusion model: mathematical definition -- 3.2 +Calculating deterministic drift and diffusion coefficients -- 3.2.1 Twisted eigenstate method -- 3.2.2 Transition matrix methods -- 3.2.3 Numerical comparison of the different methods -- 3.3 The phase diagram -- 3.4 Simple maps as deterministic ratchets -- 3.5 Summary -- 4. Deterministic reaction-diffusion -- 4.1 A reactive-diffusive multibaker map -- 4.1.1 Deterministic models of reaction-diffusion -- 4.1.2 The Frobenius-Perron operator -- 4.2 Diffusive dynamics -- 4.2.1 +Diffusive modes of the dyadic multibaker -- 4.2.2 The parameter-dependent diffusion coefficient -- 4.2.2.1 Fractal forms in the Taylor-Green-Kubo formula for dif- fusion -- 4.2.2.2 An area-preserving multibaker with a fractal diffusion co- efficient -- 4.3 Reactive dynamics -- 4.3.1 +Reactive modes of the dyadic multibaker -- 4.3.2 The parameter-dependent reaction rate -- 4.4 Summary -- 5. Deterministic diffusion and random perturbations -- 5.1 Disordered dynamical systems -- 5.2 Noisy dynamical systems -- 5.3 Summary -- 6. From normal to anomalous diffusion -- 6.1 Deterministic diffusion and bifurcations -- 6.2 Anomalous diffusion in intermittent maps -- 6.3 Summary -- 7. From diffusive maps to Hamiltonian particle billiards -- 7.1 Correlated random walks in maps -- 7.2 Correlated random walks in billiards -- 7.3 Summary.

8. Designing billiards with irregular transport coefficients -- 8.1 Diffusion in the ower-shaped billiard -- 8.2 +Random and correlated random walks -- 8.3 Diffusion in porous solids -- 8.4 Summary -- 9. Deterministic diffusion of granular particles -- 9.1 Resonances and diffusion in the bouncing ball billiard -- 9.2 +Diffusion by correlated random walks -- 9.3 Vibratory conveyors -- 9.4 Summary -- Part 2: Thermostated dynamical systems -- 10. Motivation: coupling a system to a thermal reservoir -- 10.1 Why thermostats? -- 10.2 Modeling thermal reservoirs: the Langevin equation -- 10.3 Equilibrium velocity distributions for thermostated systems -- 10.4 Applying thermostats: the periodic Lorentz gas -- 10.5 Summary -- 11. The Gaussian thermostat -- 11.1 Construction of the Gaussian thermostat -- 11.2 Chaos and transport in Gaussian thermostated systems -- 11.2.1 Phase space contraction and entropy production -- 11.2.2 Lyapunov exponents and transport coefficients -- 11.2.3 Nonequilibrium fractal attractors -- 11.2.4 Electrical conductivity -- 11.3 Summary -- 12. The Nos e-Hoover thermostat -- 12.1 The dissipative Liouville equation -- 12.2 Construction of the Nos e-Hoover thermostat -- 12.2.1 Heuristic derivation -- 12.2.2 Physics of this thermostat -- 12.3 Properties of the Nos e-Hoover thermostat -- 12.3.1 Chaos and transport -- 12.3.2 +Generalized Hamiltonian formalism -- 12.3.3 Fractals and transport -- 12.4 +Subtleties of Nose-Hoover dynamics -- 12.4.1 Necessary conditions and generalizations -- 12.4.2 Thermal reservoirs in nonequilibrium -- 12.5 Summary -- 13. Universalities in Gaussian and Nos e-Hoover dynamics? -- 13.1 Non-Hamiltonian nonequilibrium steady states -- 13.2 Phase space contraction and entropy production -- 13.3 Transport coefficients and dynamical systems quantities.

13.4 Fractal attractors for nonequilibrium steady states -- 13.5 Nonlinear response in the driven periodic Lorentz gas -- 13.6 Summary -- 14. Gaussian and Nose-Hoover thermostats revisited -- 14.1 Non-ideal Gaussian thermostat -- 14.2 Non-ideal Nose-Hoover thermostat -- 14.3 +Further alternative thermostats -- 14.4 Summary -- 15. Stochastic and deterministic boundary thermostats -- 15.1 Stochastic boundary thermostats -- 15.2 Deterministic boundary thermostats -- 15.3 +Boundary thermostats from first principles -- 15.4 Deterministic boundary thermostats for the driven periodic Lorentz gas -- 15.4.1 Phase space contraction and entropy production -- 15.4.2 Attractors, bifurcations and conductivity -- 15.4.3 Lyapunov exponents -- 15.5 Hard disk fluid under shear and heat flow -- 15.5.1 Homogeneously and inhomogeneously driven shear and heat flows -- 15.5.2 Shear and heat flows thermostated by deterministic scattering -- 15.6 Summary -- 16. Active Brownian particles and Nos e-Hoover dynamics -- 16.1 Brownian motion of migrating cells? -- 16.2 +Moving biological entities as active Brownian particles -- 16.3 +Bimodal velocity distributions and Nose-Hoover dynamics -- 16.4 Summary -- Part 3: Outlook and conclusions -- 17. Further topics in chaotic transport theory -- 17.1 Fluctuation relations -- 17.1.1 Entropy fluctuation in nonequilibrium steady states -- 17.1.2 The Gallavotti-Cohen fluctuation theorem -- 17.1.3 The Evans-Searles fluctuation theorem -- 17.1.4 Jarzynski work relation and Crooks relation -- 17.2 Lyapunov modes -- 17.3 Fourier's law -- 17.3.1 The basic problem -- 17.3.2 Heat conduction in anharmonic chaotic chains -- 17.3.3 Heat conduction in chaotic particle billiards -- 17.4 Pseudochaotic diffusion -- 17.4.1 Microscopic chaos and diffusion? -- 17.4.2 Polygonal billiard channels -- 17.5 Summary -- 18. Conclusions.

18.1 Microscopic chaos and nonequilibrium statistical mechanics: the big picture -- 18.2 Assessment of the main results -- 18.2.1 Existence of fractal transport coefficients -- 18.2.2 Universalities in thermostated dynamical systems? -- 18.3 Important open questions -- 18.3.1 Fractal transport coefficients -- 18.3.2 Thermostated dynamical systems -- Note added in proof -- Bibliography -- Index.