Nonequilibrium steady states

Kirkpatrick T R, Cohen E G D and Dorfman J R 1982 Light scattering by a fluid in a nonequilibrium steady state. II. Large gradients Phys. Rev. A 26 995... 

Holian B L 1996 The character of the nonequilibrium steady state beautiful formalism meets ugly reality Monte Carlo and Molecular Dynamics of Condensed Matter Systems, vol 49, ed K Binder and G Ciccotti (Bologna Italian Physical Society) pp 791-822... 

One shortcoming of Schild analysis is an overemphasized use of the control dose-response curve (i.e., the accuracy of every DR value depends on the accuracy of the control EC o value). An alternative method utilizes nonlinear regression of the Gaddum equation (with visualization of the data with a Clark plot [10], named for A. J. Clark). This method, unlike Schild analysis, does not emphasize control pECS0, thereby giving a more balanced estimate of antagonist affinity. This method, first described by Lew and Angus [11], is robust and theoretically more sound than Schild analysis. On the other hand, it is not as visual. Schild analysis is rapid and intuitive, and can be used to detect nonequilibrium steady states in the system that can corrupt... 

The most common method used to measure the affinity of surmountable competitive antagonists is Schild analysis. This method is visual and also is useful to detect nonequilibrium steady states in receptor preparations. 

The odd contribution to the nonequilibrium steady-state probability distribution is just the exponential of this entropy change. Hence the full nonequilibrium steady-state probability distribution is... 

From this fundamental level the model can be advanced to more complex levels. Inclusion of the dynamics of flow or transfer rates between compartments and degradation properties within compartments can transform the model to a nonequilibrium, steady state description of a chemical s fate. 

The disadvantages of the nonequilibrium steady state models have already been pointed out. In addition, evaluative models of... 

Trepagnier, E. H. Jarzynski, C. Ritort, E Crooks, G. E. Bustamante, C. J. Liphardt, J., Experimental test of Hatano and Sasa s nonequilibrium steady-state equality, Proc. Natl Acad. Set USA 2004,101, 15038-15041... 

Subotnik JE, Hansen T, Ratner MA, Nitzan A (2009) Nonequilibrium steady-state transport via the reduced density-matrix operator. J Chem Phys 130 144105... 

MSN. 100. G. Nicolis and 1. Prigogine, Irreversible processes at nonequilibrium steady states and Lyapounov functions, Proc. Natl. Acad. Sci. USA 76, 6060-6061 (1979). 

In this section, we consider a system in a nonequilibrium steady state, such as a conductor between two particle reservoirs at different chemical potentials (see Fig. 14). The state co of the system at a given time can be represented by the numbers of particles in the different cells composing the... 

The Kolmogorov-Sinai entropy per unit time is defined in Eq. (89) as the supremum of h over all the possible partitions V. Since we expect that the probability of the nonequilibrium steady state is not time-reversal symmetric, the probability of the time-reversed paths should decay at a different rate, which can be called a time-reversed entropy per unit time [3]... 

The most remarkable result is that the difference between both entropies per unit time (98) and (97) gives the entropy production of the nonequilibrium steady state ... 

Principle of Temporal Ordering. In nonequilibrium steady states, the typical paths are more ordered in time than their corresponding time reversals. 

This principle and the formula (101) show that entropy production results from a time asymmetry in the dynamical randomness in nonequilibrium steady states. 

In the limit of an arbitrarily large reservoir N,V oo with n = N/V constant, the escape rate vanishes and a nonequilibrium steady state establishes itself in the diffusive slab. 

Beside the work performed on the system, interesting quantities are the currents crossing a system in a nonequilibrium steady state. Recently, we have... 

In a nonequilibrium steady state, the entropy production is the sum of the affinities multiplied by the mean currents ... 

In nonequilibrium steady states, the mean currents crossing the system depend on the nonequilibrium constraints given by the affinities or thermodynamic forces which vanish at equihbrium. Accordingly, the mean currents can be expanded in powers of the affinities around the equilibrium state. Many nonequilibrium processes are in the linear regime studied since Onsager classical work [7]. However, chemical reactions are known to involve the nonlinear regime. This is also the case for nanosystems such as the molecular motors as recently shown [66]. In the nonlinear regime, the mean currents depend on powers of the affinities so that it is necessary to consider the full Taylor expansion of the currents on the affinities ... 

On the other hand, the nonequilibrium steady states are constructed by weighting each phase-space trajectory with a probability which is different for their time reversals. As a consequence, the invariant probability distribution describing the nonequilibrium steady state at the microscopic phase-space level explicitly breaks the time-reversal symmetry. 

It is most remarkable that the entropy production in a nonequilibrium steady state is directly related to the time asymmetry in the dynamical randomness of nonequilibrium fluctuations. The entropy production turns out to be the difference in the amounts of temporal disorder between the backward and forward paths or histories. In nonequilibrium steady states, the temporal disorder of the time reversals is larger than the temporal disorder h of the paths themselves. This is expressed by the principle of temporal ordering, according to which the typical paths are more ordered than their corresponding time reversals in nonequilibrium steady states. This principle is proved with nonequilibrium statistical mechanics and is a corollary of the second law of thermodynamics. Temporal ordering is possible out of equilibrium because of the increase of spatial disorder. There is thus no contradiction with Boltzmann s interpretation of the second law. Contrary to Boltzmann s interpretation, which deals with disorder in space at a fixed time, the principle of temporal ordering is concerned by order or disorder along the time axis, in the sequence of pictures of the nonequilibrium process filmed as a movie. The emphasis of the dynamical aspects is a recent trend that finds its roots in Shannon s information theory and modem dynamical systems theory. This can explain why we had to wait the last decade before these dynamical aspects of the second law were discovered. 

Nonequilibrium Steady State (NESS). The system is driven by external forces (either time dependent or nonconservative) in a stationary nonequilibrium state, where its properties do not change with time. The steady state is an irreversible nonequilibrium process that cannot be described by the Boltzmann-Gibbs distribution, where the average heat that is dissipated by the system (equal to the entropy production of the bath) is positive. 

There are still other categories of NESS. For example, in nonequilibrium transient steady states the system starts in a nonequilibrium steady state but is driven out of that steady state by an external perturbation to finally settle in a new steady state. 

Nonequilibrium Steady State (NESS). If the initial state is a steady state, Pxo(Co) = (0)( )- then we choose b x) = F reads... 

The nonequilibrium aging state (NBAS, see Section III.A) is a nonstationary state characterized by slow relaxation and a very low rate of energy dissipation to the surroundings. Aging systems fail to reach equilibrium unless one waits an exceedingly large amount of time. For this reason, the NEAS is very different from either the nonequilibrium transient state (NETS) or the nonequilibrium steady state (NESS). 

The polarized state (nonequilibrium steady state) is created by applying a DC voltage at an elevated temperature and by subsequent cooling of the solid to a temperature that is sufficiently low that rapid relaxation is prevented. The next step of the experimental procedure is to remove the DC bias. The currents that can be measured during either isothermal or nonisothermal relaxation back to thermal equilibrium are used to monitor the relaxation processes involved. 

Under those conditions P behaves as a Lagrangian in mechanics. Furthermore, as P is a nonnegative function for any positive value of the concentrations X,, by a theorem due to Lyapounov, the asymptotic stability of nonequilibrium steady states is ensured (theorem of minimum entropy production.1-23 These steady states are thus characterized by a minimum level of the dissipation in the linear domain of nonequilibrium thermodynamics the systems tend to states approaching equilibrium as much as their constraints permit. Although entropy may be lower than at equilibrium, the equilibrium type of order still prevails. The steady states belong to what has been called the thermodynamic branch, as it contains the equilibrium state as a particular case. 

A stability criterion for nonequilibrium steady states can readily be deduced from (9). Suppose that for all small departures from the steady state considered we have... 

There are two more important advantages of these models. One is that it is possible under some conditions to carry out an exact stability analysis of the nonequilibrium steady-state solutions and to determine points of exchange of stability corresponding to secondary bifurcations on these branches. The other is that branches of solutions can be calculated that are not accessible by the usual approximate methods. We have already seen a case here in which the values of parameters correspond to domain 2. This also happens when the fixed boundary conditions imposed on the system are arbitrary and do not correspond to some homogeneous steady-state value of X and Y. In that case Fig. 20 may, for example,... 

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