Ruelle's thermodynamic formalism assigns a dynamical partition function to a chaotic system by raising its expansion factor along unstable manifolds to a power 1- β, and averaging over all initial points on the relevant shell in phase space. For a closed system its logarithm over t, usually called the topological pressure, yields the Kolmogorov-Sinai entropy as a derivative at β=1, and is called the topological entropy for β=0. For open systems the thermodynamic pressure at β=1 also gives the average escape rate from the system.

For a dilute disordered Lorentz gas at equilibrium (that is, a system of fixed hard spherical scatterers with one light particle moving elastically among them) the thermodynamic pressure may be calculated explicitly, yielding results in agreement with previous calculations. For β-values different from unity the topological pressure for large enough systems always becomes dominated by orbits confined either to the direct neighborhood of a periodic orbit or to a small subspace with a higher than average collision rate. For example the topological entropy with increasing system size soon is determined exclusively by orbits confined to a very small subsystem of the total system.

In the presence of a driving field combined with a gaussian thermostat the calculation of the dynamic partition function involves a simple transfer matrix formalism. The same holds for a system with open boundaries. In the latter case it is helpful mapping the problem to a random flight model with escape through the boundaries.