On time's arrow in Ehrenfest models with reversible deterministic dynamics

We introduce a deterministic, time-reversible version of the Ehrenfest urn model. The distribution of first-passage times from equilibrium to non-equilibrium states and vice versa is calculated. We find that average times for transition to non-equilibrium always scale exponentially with the system size, whereas the time scale for relaxation to equilibrium depends on microscopic dynamics. To illustrate this, we also look at deterministic and stochastic versions of the Ehrenfest model with a distribution of microscopic relaxation times.Comment: 6 pages, 7 figures, revte

Effect of phonon-phonon interactions on localization

We study the heat current J in a classical one-dimensional disordered chain with on-site pinning and with ends connected to stochastic thermal reservoirs at different temperatures. In the absence of anharmonicity all modes are localized and there is a gap in the spectrum. Consequently J decays exponentially with system size N. Using simulations we find that even a small amount of anharmonicity leads to a J~1/N dependence, implying diffusive transport of energy.Comment: 4 pages, 2 figures, Published versio

Heat conduction in disordered harmonic lattices with energy conserving noise

We study heat conduction in a harmonic crystal whose bulk dynamics is supplemented by random reversals (flips) of the velocity of each particle at a rate $\lambda$. The system is maintained in a nonequilibrium stationary state(NESS) by contacts with Langevin reservoirs at different temperatures. We show that the one-body and pair correlations in this system are the same (after an appropriate mapping of parameters) as those obtained for a model with self-consistent reservoirs. This is true both for the case of equal and random(quenched) masses. While the heat conductivity in the NESS of the ordered system is known explicitly, much less is known about the random mass case. Here we investigate the random system, with velocity flips. We improve the bounds on the Green-Kubo conductivity obtained by C.Bernardin. The conductivity of the 1D system is then studied both numerically and analytically. This sheds some light on the effect of noise on the transport properties of systems with localized states caused by quenched disorder.Comment: 19 pages, 8 figure

A Remedy for Rule 238

Rule 238 of the Pennsylvania Rules of Civil Procedure was promulgated in 1979 in an attempt to encourage parties to settle their cases as early as possible in order to avoid the costs, both to the court system and to the litigants themselves, of litigation. Seven years later this experiment was deemed a failure, for in Craig v. Magee Memorial Rehabilitation Center the Supreme Court of Pennsylvania declared the Rule to be unconstitutional and therefore suspended its operation. In this same opinion, the court directed the Civil Procedure Rules Committee to propose an amended version of the Rule for its consideration. The author argues that the only way Rule 238 will be able to meet its original expectations is if the Committee overhauls the Rule by amending the already existing delay damages provision and combining it with a costs provision similar to the one found in F. R. Ctv. P. 68