Nonequilibrium dynamics

J. Krug, M. Schimschak. J Phys (France) I 5 1065, 1995 J. Krug. In A. McKane, M. Droz, J. Vannimenus, D. Wolf, eds. Scale Invariance, Interfaces and Nonequilibrium Dynamics. New York Plenum Press 1995. 

It should be clear that the most likely or physical rate of first entropy production is neither minimal nor maximal these would correspond to values of the heat flux of oc. The conventional first entropy does not provide any variational principle for heat flow, or for nonequilibrium dynamics more generally. This is consistent with the introductory remarks about the second law of equilibrium thermodynamics, Eq. (1), namely, that this law and the first entropy that in invokes are independent of time. In the literature one finds claims for both extreme theorems some claim that the rate of entropy production is... 

The next three chapters deal with the most widely used classes of methods free energy perturbation (FEP) [3], methods based on probability distributions and histograms, and thermodynamic integration (TI) [1, 2], These chapters represent a mix of traditional material that has already been well covered, as well as the description of new techniques that have been developed only recendy. The common thread followed here is that different methods share the same underlying principles. Chapter 5 is dedicated to a relatively new class of methods, based on calculating free energies from nonequilibrium dynamics. In Chap. 6, we discuss an important topic that has not received, so far, sufficient attention - the analysis of errors in free energy calculations, especially those based on perturbative and nonequilibrium approaches. 

On several occasions, the reader will notice a direct connection between the topics covered in the book and other, related areas of statistical mechanics, such as the methodology of computer simulations, nonequilibrium dynamics or chemical kinetics. This is hardly a surprise because free energy calculations are at the nexus of statistical mechanics of condensed phases. 

Most of the theoretical works concerning dynamical aspects of chemical reactions are treated within the adiabatic approximation, which is based on the assumption that the solvent instantaneously adjusts itself to any change in the solute charge distribution. However, in certain conditions, such as sudden perturbations or long solvent relaxation times, the total polarization of the solvent is no longer equilibrated with the actual solute charge distribution and cannot be properly described by the adiabatic approximation. In such a case, the reacting system is better described by nonequilibrium dynamics. 

Many different types of materials were later shown to exhibit aging and nonequilibrium dynamics, including polymers [91], orientational glasses [92], gels [93], and ceramic superconductors [94]. 

Aging and nonequilibrium dynamics indicate but give by no means evidence for a thermodynamic phase transition at finite temperamre to a low-temperature... 

A. V. Einkelstein, Proteins structural, thermodynamic and kinetic aspects, in Slow Relaxations arul Nonequilibrium Dynamics (J. L. Barrat and J. Kurchan, eds.) Springer-Verlag, Berlin, 2004, pp. 650-703. 

In the bottom-up approach, a large variety of ordered nano-, micro-and macrostructures may be obtained by changing the balance of all the attractive and repulsive forces between the structure-forming molecules or particles. This can be achieved by altering the environmental conditions (temperature, pH, ionic strength, presence of specific substances or ions) and the concentration of molecules/particles in the system (Min et al., 2008). As this takes place, the interrelated processes of formation and stabilization are both important considerations in the production of nanoparticles. In addition, as particles grow in size a number of intrinsic properties change, some qualitatively, others quantitatively some affect the equilibrium (thermodynamic) properties, and others affect the nonequilibrium (dynamic) properties such as relaxation times. 

Cates, M. E. Evans, M. R. (eds.) Soft and Fragile Matter, Nonequilibrium Dynamics, Metastability and Flow (IOP Bristol, UK, 2000). 

L. F. Cugliandolo, Dynamics of glassy systems, in Slow Relaxations and Nonequilibrium Dynamics in Condensed Matter, Les Houches—Ecole d Ete de Physique Theorique, Vol. 

L. F. Cugliandolo and G. Lozano, Real-time nonequilibrium dynamics of quantum glassy systems. Phys. Rev. B 59, 915 (1999). 

It seems reasonable to expand ideas of thermodynamics over strongly nonequilibrium dynamic systems because the thermodynamic approach allows a number of questions on the state or course of the system evolution to be answered, even when knowledge of the real kinetic scheme of the dynamic process under consideration is limited or incomplete. Here, typi cal problems are those that involve finding probable stationary states. Such problems relate usually to the solution of another principal problem—that is, whether the knowledge of only some or a few of the kinetic peculiarities of the reaction system is sufficient for predicting, based on thermodynamic... 

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