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