Estimating Probability weights of Deterministic many-body Systems in their Steady States

Seminar | March 24 | 2-4 p.m. | 775B Tan Hall

 Dr. Zdenek Preisler, LBNL

 College of Chemistry

Observations of phenomena like phase separation in non-equilibrium steady states, similar to those found in equilibrium systems motivates attempts to rigorously estimate the probability distribution of the underlying states.
Here, we numerically investigate the probability measures of deterministic i) equilibrium systems and ii) out-of-equilibrium systems in their steady states, for which the Boltzmann-Gibb measure is not valid.
In particular we are motivated by results of Tuckerman et. al. [1] on the isokinetic ensemble together with the works on the fluctuation theorem by Evans et al. [2], and Gallavotti et al. [3] pointing out the possible significance of the dynamical measures introduced by Sinai, Ruelle and Bowen [4].
Unfortunately, these dynamical measures are computationally difficult to determine.
Nevertheless, we show that due to the advancement in computational power one can use these to numerically estimate probability weights of strongly chaotic deterministic systems using brute force.
Specifically, we study deterministic many-body systems with isokinetic (equilibrium) and SLLOD (shear) equations of motions.
First, we recover the Boltzmann factor for isokinetic ensemble verifying validity of our approach and then we apply the methodology to obtain probability weights of a system under shear.

[1] M. E. Tuckerman, C. J. Mundy and G. J. Martyna, EPL (Europhysics Letters), 1999, 45, 149.
[2] D. J. Evans, E. G. D. Cohen and G. P. Morriss, Phys. Rev. Lett., 1993, 71, 2401–2404.
[3] G. Gallavotti and E. G. D. Cohen, Phys. Rev. Lett., 1995, 74, 2694–2697.
[4] J. P. Eckmann and D. Ruelle, Rev. Mod. Phys., 1985, 57, 617–656.