Symmetry relations in chemical kinetics arising from microscopic reversibility

It is shown that the kinetics of time-reversible chemical reactions having the same equilibrium constant but different initial conditions are closely related to one another by a directly measurable symmetry relation analogous to chemical detailed balance. In contrast to detailed balance, however, this relation does not require knowledge of the elementary steps that underlie the reaction, and remains valid in regimes where the concept of rate constants is ill-defined, such as at very short times and in the presence of low activation barriers. Numerical simulations of a model of isomerization in solution are provided to illustrate the symmetry under such conditions, and potential applications in protein folding-unfolding are pointed out.Comment: 4 pages, 1 figure, accepted to Phys Rev Let

Elastic Energy, Fluctuations and Temperature for Granular Materials

We probe, using a model system, elastic and kinetic energies for sheared granular materials. For large enough $P/E_y$ (pressure/Young's modulus) and $P/\rho v^2$ ($P/$kinetic energy density) elastic dominates kinetic energy, and energy fluctuations become primarily elastic in nature. This regime has likely been reached in recent experiments. We consider a generalization of the granular temperature, $T_g$, with both kinetic and elastic terms and that changes smoothly from one regime to the other. This $T_g$ is roughly consistent with a temperature adapted from equilibrium statistical mechanics.Comment: 4 pages, 4 figure

A generalized Chudley-Elliott vibration-jump model in activated atom surface diffusion

Here the authors provide a generalized Chudley-Elliott expression for activated atom surface diffusion which takes into account the coupling between both low-frequency vibrational motion (namely, the frustrated translational modes) and diffusion. This expression is derived within the Gaussian approximation framework for the intermediate scattering function at low coverage. Moreover, inelastic contributions (arising from creation and annihilation processes) to the full width at half maximum of the quasi-elastic peak are also obtained.Comment: (5 pages, 2 figures; revised version

Field theory fo charged fluids and colloids

A systematic field theory is presented for charged systems. The one-loop level corresponds to the classical Debye-H\"uckel (DH) theory, and exhibits the full hierarchy of multi-body correlations determined by pair-distribution functions given by the screened DH potential. Higher-loop corrections can lead to attractive pair interactions between colloids in asymmetric ionic environments. The free energy follows as a loop-wise expansion in half-integer powers of the density; the resulting two-phase demixing region shows pronounced deviations from DH theory for strongly charged colloids.Comment: 4 pages, 2 ps figs; new version corrects some minor typo

Effective Confinement as Origin of the Equivalence of Kinetic Temperature and Fluctuation-Dissipation Ratio in a Dense Shear Driven Suspension

We study response and velocity autocorrelation functions for a tagged particle in a shear driven suspension governed by underdamped stochastic dynamics. We follow the idea of an effective confinement in dense suspensions and exploit a time-scale separation between particle reorganization and vibrational motion. This allows us to approximately derive the fluctuation-dissipation theorem in a "hybrid" form involving the kinetic temperature as an effective temperature and an additive correction term. We show numerically that even in a moderately dense suspension the latter is negligible. We discuss similarities and differences with a simple toy model, a single trapped particle in shear flow

Phonon Life-times from first principles self consistent lattice dynamics

Phonon lifetime calculations from first principles usually rely on time consuming molecular dynamics calculations, or density functional perturbation theory (DFPT) where the zero temperature crystal structure is assumed to be dynamically stable. Here a new and effective method for calculating phonon lifetimes from first principles is presented, not limited to crystal structures stable at 0 K, and potentially much more effective than most corresponding molecular dynamics calculations. The method is based on the recently developed self consistent lattice dynamical method and is here tested by calculating the bcc phase phonon lifetimes of Li, Na, Ti and Zr, as representative examples.Comment: 4 pages, 4 figur

Transfer Entropy as a Log-likelihood Ratio

Transfer entropy, an information-theoretic measure of time-directed information transfer between joint processes, has steadily gained popularity in the analysis of complex stochastic dynamics in diverse fields, including the neurosciences, ecology, climatology and econometrics. We show that for a broad class of predictive models, the log-likelihood ratio test statistic for the null hypothesis of zero transfer entropy is a consistent estimator for the transfer entropy itself. For finite Markov chains, furthermore, no explicit model is required. In the general case, an asymptotic chi-squared distribution is established for the transfer entropy estimator. The result generalises the equivalence in the Gaussian case of transfer entropy and Granger causality, a statistical notion of causal influence based on prediction via vector autoregression, and establishes a fundamental connection between directed information transfer and causality in the Wiener-Granger sense

Diffusion-Limited Coalescence with Finite Reaction Rates in One Dimension

We study the diffusion-limited process $A+A\to A$ in one dimension, with finite reaction rates. We develop an approximation scheme based on the method of Inter-Particle Distribution Functions (IPDF), which was formerly used for the exact solution of the same process with infinite reaction rate. The approximation becomes exact in the very early time regime (or the reaction-controlled limit) and in the long time (diffusion-controlled) asymptotic limit. For the intermediate time regime, we obtain a simple interpolative behavior between these two limits. We also study the coalescence process (with finite reaction rates) with the back reaction $A\to A+A$, and in the presence of particle input. In each of these cases the system reaches a non-trivial steady state with a finite concentration of particles. Theoretical predictions for the concentration time dependence and for the IPDF are compared to computer simulations. P. A. C. S. Numbers: 82.20.Mj 02.50.+s 05.40.+j 05.70.LnComment: 13 pages (and 4 figures), plain TeX, SISSA-94-0

Multiscaling for Systems with a Broad Continuum of Characteristic Lengths and Times: Structural Transitions in Nanocomposites

The multiscale approach to N-body systems is generalized to address the broad continuum of long time and length scales associated with collective behaviors. A technique is developed based on the concept of an uncountable set of time variables and of order parameters (OPs) specifying major features of the system. We adopt this perspective as a natural extension of the commonly used discrete set of timescales and OPs which is practical when only a few, widely-separated scales exist. The existence of a gap in the spectrum of timescales for such a system (under quasiequilibrium conditions) is used to introduce a continuous scaling and perform a multiscale analysis of the Liouville equation. A functional-differential Smoluchowski equation is derived for the stochastic dynamics of the continuum of Fourier component order parameters. A continuum of spatially non-local Langevin equations for the OPs is also derived. The theory is demonstrated via the analysis of structural transitions in a composite material, as occurs for viral capsids and molecular circuits.Comment: 28 pages, 1 figur

Random walk approach to the d-dimensional disordered Lorentz gas

A correlated random walk approach to diffusion is applied to the disordered nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic expression for the diffusion constant in arbitrary number of dimensions d is obtained. The result corresponds to an Enskog-like correction to the Boltzmann prediction, being exact in the dilute limit, and better or nearly exact in comparison to renormalized kinetic theory predictions for all allowed densities in d=2,3. Extensive numerical simulations were also performed to elucidate the role of the approximations involved.Comment: 5 pages, 5 figure