SMS scnews item created by Georg Gottwald at Wed 20 Jun 2007 1217
Type: Seminar
Distribution: World
Expiry: 26 Jun 2007
Calendar1: 26 Jun 2007 1600-1700
CalLoc1: UNSW Physics Common Room 64
CalTitle1: GORDON GODFREY SEMINARat UNSW: Henk van Beijeren -- On the connections between chaos theory and statistical mechanics
Auth: gottwald@p6363.pc.maths.usyd.edu.au

# GORDON GODFREY SEMINAR at UNSW: Henk van Beijeren -- On the connections between chaos theory and statistical mechanics

 GORDON GODFREY SEMINAR 26 JUNE UNSW Physics Common Room 64 at 4 pm

On the connections between chaos theory and statistical mechanics

Professor Henk van Beijeren, Institute for Theoretical Physics, Utrecht University

The past years have seen a surge of activity on the connections between chaos theory and
statistical mechanics.  Among the connections known I want to mention: 1) the Gaussian
thermostat formalism, developed by Hoover, Evans et al.  Here the irreversible entropy
production in a stationary non-equilibrium system is related to the sum of all of its
Lyapunov exponents.  2) the escape-rate formalism of Gaspard and and Nicolis, in which
transport coefficients determining the rate of escape of systems from phase space
through an open boundary are related tot the Kolmogorov-Sinai entropy and the sum of all
positive Lyapunov exponents on a small subset of phase space.  3) Ruelle’s thermodynamic
formalism, in which chaotic as well as transport properties can be obtained from a
single dynamical partition function.  This is even more ambitious, but for the majority
of many-particle systems calculation of the dynamical partition function is a very hard

Here I will briefly introduce dynamical systems and discuss their characteristic
properties.  I will show how quantities like Lyapunov exponents, Kolmogorov-Sinai
entropies and topological pressures may be calculated for a dilute Lorentz gas
(disordered billiard), which is a system with fixed scatterers on random positions, with
which a point particle makes elastic collisions.  Comparisons of the results with
computer simulation results show a very good agreement.

For a dilute hard sphere gas in equilibrium both the KS entropy (equal to the sum of all
positive Lyapunov exponents) and the largest Lyapunov exponent can be calculated
analytically to leading orders in the density.  Again, comparisons to computer
simulations show good agreement.  The smallest positive Lyapunov exponents for these
systems show very interesting collective behavior, which can also be explained through
kinetic theory calculations.

Finally I will discuss some outstanding open problems.

Wine and cheese at 3.45 pm.


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