Forcing anomalous scaling on demographic fluctuations

We discuss the conditions under which a population of anomalously diffusing individuals can be characterized by demographic fluctuations that are anomalously scaling themselves. Two examples are provided in the case of individuals migrating by Gaussian diffusion, and by a sequence of L\'evy flights.Comment: 5 pages 2 figure

Accelerating the convergence of path integral dynamics with a generalized Langevin equation

The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasi-harmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water

Correlation function and generalized master equation of arbitrary age

We study a two-state statistical process with a non-Poisson distribution of sojourn times. In accordance with earlier work, we find that this process is characterized by aging and we study three different ways to define the correlation function of arbitrary age of the corresponding dichotomous fluctuation based respectively on the Generalized Master Equation formalism, on a Liouville-like approach and on a trajectory perspective.Comment: 11 pages, 1figur

Efficient stochastic thermostatting of path integral molecular dynamics

The path integral molecular dynamics (PIMD) method provides a convenient way to compute the quantum mechanical structural and thermodynamic properties of condensed phase systems at the expense of introducing an additional set of high-frequency normal modes on top of the physical vibrations of the system. Efficiently sampling such a wide range of frequencies provides a considerable thermostatting challenge. Here we introduce a simple stochastic path integral Langevin equation (PILE) thermostat which exploits an analytic knowledge of the free path integral normal mode frequencies. We also apply a recently-developed colored-noise thermostat based on a generalized Langevin equation (GLE), which automatically achieves a similar, frequency-optimized sampling. The sampling efficiencies of these thermostats are compared with that of the more conventional Nos\'e-Hoover chain (NHC) thermostat for a number of physically relevant properties of the liquid water and hydrogen-in-palladium systems. In nearly every case, the new PILE thermostat is found to perform just as well as the NHC thermostat while allowing for a computationally more efficient implementation. The GLE thermostat also proves to be very robust delivering a near-optimum sampling efficiency in all of the cases considered. We suspect that these simple stochastic thermostats will therefore find useful application in many future PIMD simulations.Comment: Accepted for publication on JC

Transport Coefficients of Non-Newtonian Fluid and Causal Dissipative Hydrodynamics

A new formula to calculate the transport coefficients of the causal dissipative hydrodynamics is derived by using the projection operator method (Mori-Zwanzig formalism) in [T. Koide, Phys. Rev. E75, 060103(R) (2007)]. This is an extension of the Green-Kubo-Nakano (GKN) formula to the case of non-Newtonian fluids, which is the essential factor to preserve the relativistic causality in relativistic dissipative hydrodynamics. This formula is the generalization of the GKN formula in the sense that it can reproduce the GKN formula in a certain limit. In this work, we extend the previous work so as to apply to more general situations.Comment: 15 pages, no figure. Discussions are added in the concluding remarks. Accepted for publication in Phys. Rev.

The geometry of thermodynamic control

A deeper understanding of nonequilibrium phenomena is needed to reveal the principles governing natural and synthetic molecular machines. Recent work has shown that when a thermodynamic system is driven from equilibrium then, in the linear response regime, the space of controllable parameters has a Riemannian geometry induced by a generalized friction tensor. We exploit this geometric insight to construct closed-form expressions for minimal-dissipation protocols for a particle diffusing in a one dimensional harmonic potential, where the spring constant, inverse temperature, and trap location are adjusted simultaneously. These optimal protocols are geodesics on the Riemannian manifold, and reveal that this simple model has a surprisingly rich geometry. We test these optimal protocols via a numerical implementation of the Fokker-Planck equation and demonstrate that the friction tensor arises naturally from a first order expansion in temporal derivatives of the control parameters, without appealing directly to linear response theory

Solidity of viscous liquids. IV. Density fluctuations

This paper is the fourth in a series exploring the physical consequences of the solidity of highly viscous liquids. It is argued that the two basic characteristics of a flow event (a jump between two energy minima in configuration space) are the local density change and the sum of all particle displacements. Based on this it is proposed that density fluctuations are described by a time-dependent Ginzburg-Landau equation with rates in k-space of the form $\Gamma_0+Dk^2$ with $D\gg\Gamma_0a^2$ where $a$ is the average intermolecular distance. The inequality expresses a long-wavelength dominance of the dynamics which implies that the Hamiltonian (free energy) may be taken to be ultra local. As an illustration of the theory the case with the simplest non-trivial Hamiltonian is solved to second order in the Gaussian approximation, where it predicts an asymmetric frequency dependence of the isothermal bulk modulus with Debye behavior at low frequencies and an $\omega^{-1/2}$ decay of the loss at high frequencies. Finally, a general formalism for the description of viscous liquid dynamics, which supplements the density dynamics by including stress fields, a potential energy field, and molecular orientational fields, is proposed

Phase transition in the Jarzynski estimator of free energy differences

The transition between a regime in which thermodynamic relations apply only to ensembles of small systems coupled to a large environment and a regime in which they can be used to characterize individual macroscopic systems is analyzed in terms of the change in behavior of the Jarzynski estimator of equilibrium free energy differences from nonequilibrium work measurements. Given a fixed number of measurements, the Jarzynski estimator is unbiased for sufficiently small systems. In these systems, the directionality of time is poorly defined and configurations that dominate the empirical average, but which are in fact typical of the reverse process, are sufficiently well sampled. As the system size increases the arrow of time becomes better defined. The dominant atypical fluctuations become rare and eventually cannot be sampled with the limited resources that are available. Asymptotically, only typical work values are measured. The Jarzynski estimator becomes maximally biased and approaches the exponential of minus the average work, which is the result that is expected from standard macroscopic thermodynamics. In the proper scaling limit, this regime change can be described in terms of a phase transition in variants of the random energy model (REM). This correspondence is explicitly demonstrated in several examples of physical interest: near-equilibrium processes in which the work distribution is Gaussian, the sudden compression of an ideal gas and adiabatic quasi-static volume changes in a dilute real gas.Comment: 29 pages, 5 figures, accepted for publication in Physical Review E (2012

Gaussian density fluctuations and Mode Coupling Theory for supercooled liquids

The equations of motion for the density modes of a fluid, derived from Newton's equations, are written as a linear generalized Langevin equation. The constraint imposed by the fluctuation-dissipation theorem is used to derive an exact form for the memory function. The resulting equations, solved under the assumption that the noise, and consequently density fluctuations, of the liquid are gaussian distributed, are equivalent to the random-phase-approximation for the static structure factor and to the well known ideal mode coupling theory (MCT) equations for the dynamics. This finding suggests that MCT is the canonical mean-field theory of the fluid dynamics.Comment: 4 pages, REVTE

Forces Induced by Non-Equilibrium Fluctuations: The Soret-Casimir Effect

The notion of fluctuation-induced forces is generalized to the cases where the fluctuations have nonequilibrium origin. It is shown that a net force is exerted on a single flat plate that restricts scale-free fluctuations of a scalar field in a temperature gradient. This force tends to push the object to the colder regions, which is a manifestation of thermophoresis or the Soret effect. In the classic two-plate geometry, it is shown that the Casimir forces exerted on the two plates differ from each other, and thus the Newton's third law is violated.Comment: 8 pages, 5 postscript figures, uses (old) RevTe