This paper is a review of results which have been recently obtained by applying mathematical
concepts drawn, in particular, from differential geometry and topology, to the physics of …

The phase behavior at low temperature, in particular the critical and tricritical properties, of
liquid 3 He 4 He mixtures and certain types of metamagnets — a class of highly anisotropic …

We propose a new definition of natural invariant measure for trajectory segments of finite
duration for a many-particle system. On this basis we give an expression for the probability of …

Ruelle's principle for turbulence leading to what is usually called the Sinai-Ruelle-Bowen (SRB)
distribution is applied to the statistical mechanics of many particle systems in …

We consider nonequilibrium systems with complex dynamics in stationary states with large
fluctuations of intensive quantities (eg the temperature, chemical potential or energy …

We propose, as a generalization of an idea of Ruelle's to describe turbulent fluid flow, a chaotic
hypothesis for reversible dissipative many-particle systems in nonequilibrium stationary …

Heat fluctuations are studied in a dissipative system with both deterministic and stochastic
components for a simple model: a Brownian particle dragged through water by a moving …

Velocity correlation functions ρ (t) in hard-disk and hard-sphere fluids are discussed on the
basis of the kinetic theory of gases. It is found in d dimensions that ρ (t)∼ α (tt 0)− d 2 with α= …

Recently Wang et al. carried out a laboratory experiment, where a Brownian particle was
dragged through a fluid by a harmonic force with constant velocity of its center. This experiment …

Complex nonequilibrium systems are often effectively described by a “statistics of a statistics”,
in short, a “superstatistics”. We describe how to proceed from a given experimental time …