Statistical mechanics far from equilibrium: prediction and test for a sheared system.

We report the application of a far-from-equilibrium statistical-mechanical theory to a nontrivial system with Newtonian interactions in continuous boundary-driven flow. By numerically time stepping the force-balance equations of a one-dimensional model fluid we measure occupancies and transition rates in simulation. The high-shear-rate simulation data reproduce the predicted invariant quantities, thus supporting the theory that a class of nonequilibrium steady states of matter, namely, sheared complex fluids, is amenable to statistical treatment from first principles.

Steady-state work fluctuations of a dragged particle under external and thermal noise.

We consider a particle, confined to a moving harmonic potential, under the influence of friction and external asymmetric Poissonian shot noise (PSN). We study the fluctuations of the work done to maintain this system in a nonequilibrium steady state. PSN generalizes the usual Gaussian noise and can be considered to be a paradigm of external noise, where fluctuation and dissipation originate from physically independent mechanisms. We consider two scenarios: (i) the noise is given purely by PSN and (ii) in addition to PSN the particle is subject to white Gaussian noise. In both cases we derive exact expressions for the large deviation form of the work distribution, which are characterized by the time scales of the system. We show that the usual steady-state fluctuation theorem does not apply in our model and that in a certain parameter regime large negative work fluctuations are more likely to occur than the corresponding positive ones, though the average work is always positive.

Fluctuation properties of an effective nonlinear system subject to Poisson noise.

We study the work fluctuations of a particle, confined to a moving harmonic potential, under the influence of friction and external asymmetric Poissonian shot noise. This type of noise generalizes the usual Gaussian noise and induces an effective interaction between the noise and the potential, leading to an effectively nonlinear system with singular features. On the basis of an analytic solution we investigate the roles of time scales, symmetries, and singularities in the context of nonequilibrium fluctuations. Our results highlight the nonuniversality of the steady-state fluctuation theorem in stochastic systems.

Prevalence of diagnosed and undiagnosed diabetes mellitus and impaired fasting glucose in Sardinia.

We aimed at updating the prevalence of impaired fasting glucose (IFG) and of undiagnosed (UD) and diagnosed diabetes (DD) among the Sardinian population. The survey was carried out from 2002 to 2005 on 4.737 subjects aged 20-80+ years. IFG was diagnosed when blood glucose was 110-125 mg/dl; UD when it was >or=126 mg/dl in the absence of personal history of diabetes; DD when personal history was positive, irrespective of blood glucose value. Prevalence rates (%) were adjusted for age by direct method to the Italian 2001 population. IFG was diagnosed in 11% of the sample (9.88% in females and 12.24% in males); UD was found in 5.65% (5.20 and 6.15%, females and males, respectively), DD in 8.72% (6.74 and 10.05%); and total diabetes (TD), i.e. the sum of UD + DD, was 14.37% (12.93 and 15.07%, females and males, respectively). In Sardinia, in about 5 years there was an increase of IFG (+61.8%), UD (+56.9%), DD (+55.7%), and TD (+57.9%). Thus Sardinia participates in the worldwide increase in prevalence of diabetes and its microvascular, macrovascular, and socioeconomic consequences.

Invariant quantities in shear flow.

The dynamics of systems out of thermal equilibrium is usually treated on a case-by-case basis without knowledge of fundamental and universal principles. We address this problem for a class of driven steady states, namely, those mechanically driven at the boundaries such as complex fluids under shear. From a nonequilibrium counterpart to detailed balance (NCDB) we derive a remarkably simple set of invariant quantities which remain unchanged when the system is driven. These new nonequilibrium relations are both exact and valid arbitrarily far from equilibrium. Furthermore, they enable the systematic calculation of transition rates in driven systems with state spaces of arbitrary connectivity.

Properties of a nonequilibrium heat bath.

At equilibrium, a fluid element, within a larger heat bath, receives random impulses from the bath. Those impulses, which induce stochastic transitions in the system (the fluid element), respect the principle of detailed balance, because the bath is also at equilibrium. Under continuous shear, the fluid element adopts a nonequilibrium steady state. Because the surrounding bath of fluid under shear is also in a nonequilibrium steady state, the system receives stochastic impulses with a nonequilibrium distribution. Those impulses no longer respect detailed balance, but are nevertheless constrained by rules. The rules in question, which are applicable to a wide subclass of driven steady states, were recently derived [R. M. L. Evans, Phys. Rev. Lett. 92, 150601 (2004); J. Phys A 38, 293 (2005)] using information-theoretic arguments. In the present paper, we provide a more fundamental derivation, based on the uncontroversial, non-Bayesian interpretation of probabilities as simple ratios of countable quantities. We apply the results to some simple models of interacting particles, to investigate the nature of forces that are mediated by a nonequilibrium noise source such as a fluid under shear.

Exact solution of a generalized Kramers-Fokker-Planck equation retaining retardation effects.

In order to describe non-Gaussian kinetics in weakly damped systems, the concept of continuous time random walks is extended to particles with finite inertia. One thus obtains a generalized Kramers-Fokker-Planck equation, which retains retardation effects, i.e., nonlocal couplings in time and space. It is shown that despite this complexity, exact solutions of this equation can be given in terms of superpositions of Gaussian distributions with varying variances. In particular, the long-time behavior of the respective low-order moments is calculated.

Anomalous diffusion of inertial, weakly damped particles.

The anomalous (i.e., non-Gaussian) dynamics of particles subject to a deterministic acceleration and a series of "random kicks" is studied. Based on an extension of the concept of continuous time random walks to position-velocity space, a new fractional equation of the Kramers-Fokker-Planck type is derived. The associated collision operator necessarily involves a fractional substantial derivative, representing important nonlocal couplings in time and space. For the force-free case, a closed solution is found and discussed.

Validation of the Jarzynski relation for a system with strong thermal coupling: an isothermal ideal gas model.

We revisit the paradigm of an ideal gas under isothermal conditions. A moving piston performs work on an ideal gas in a container that is strongly coupled to a heat reservoir. The thermal coupling is modeled by stochastic scattering at the boundaries. In contrast to recent studies of an adiabatic ideal gas with a piston [R.C. Lua and A.Y. Grosberg, J. Phys. Chem. B 109, 6805 (2005); I. Bena, Europhys. Lett. 71, 879 (2005)], the container and piston stay in contact with the heat bath during the work process. Under this condition the heat reservoir as well as the system depend on the work parameter lambda and microscopic reversibility is broken for a moving piston. Our model is thus not included in the class of systems for which the nonequilibrium work theorem has been derived rigorously either by Hamiltonian [C. Jarzynski, J. Stat. Mech. (2004) P09005] or stochastic methods [G.E. Crooks, J. Stat. Phys. 90, 1481 (1998)]. Nevertheless the validity of the nonequilibrium work theorem is confirmed both numerically for a wide range of parameter values and analytically in the limit of a very fast moving piston, i.e., in the far nonequilibrium regime.

Joint probability distributions for a class of non-Markovian processes.

We consider joint probability distributions for the class of coupled Langevin equations introduced by Fogedby [H. C. Fogedby, Phys. Rev. E 50, 1657 (1994)]. We generalize well-known results for the single-time probability distributions to the case of N -time joint probability distributions. It is shown that these probability distribution functions can be obtained by an integral transform from distributions of a Markovian process. The integral kernel obeys a partial differential equation with fractional time derivatives reflecting the non-Markovian character of the process.