Deterministic chaos and
nonequilibrium statistical mechanics:
outline of contents

0.

Introduction

list of references

table of contents

overview: models and key ideas

1.

Basic concepts of dynamical systems theory

deterministic chaos in piecewise linear maps

Lyapunov exponents, dynamical entropies, and fractal dimensions

probability measures and the FrobeniusPerron equation

2.

Chaotic diffusion

random walks

diffusion equation and escape rate formalism

GreenKubo formula and fractal functions

thermodynamic formalism

cycle expansion methods

anomalous diffusion

3.

Chaotic currents and chaotic reactiondiffusion

linear and nonlinear response in simple biased maps

Langevin equations, ratchets, and molecular motors

reactiondiffusion systems

4.

Disordered dynamical systems

quenched disorder and subdiffusion

diffusion on disordered lattices

chaotic diffusion and noise

5.

Chaotic transport in multibaker maps

ergodic properties, dynamical systems classifications, and timereversibility

relation between onedimensional maps and baker maps

diffusive multibaker maps

biased multibaker maps and entropy production

6.

Chaotic diffusion in the periodic Lorentz gas

definition of the model and dynamical properties

relation between the periodic Lorentz gas and twodimensional maps

analysis of the densitydependent diffusion coefficient

Boltzmann equation, kinetic theory, and Lyapunov exponents

7.

the thermostated systems approach to nonequilibrium steady states

the Gaussian thermostated Lorentz gas

chaotic and fractal properties of nonequilibrium steady states in thermostated
systems

the NoseHoover thermostat, generalized Liouville equation, and generalized
Hamiltonian formalism

criticism of this approach

8.

the thermostated systems approach revisited

nonideal Gaussian and NoseHoover thermostats

stochastic boundary conditions

thermostating by deterministic scattering

do there exist universal chaotic and fractal properties of thermostated
nonequilibrium steady states?

deterministic thermostats, active Brownian particles, and cell motility

9.

fluctuation theorems

10.

entropies
and microscopic chaos in experiments?