Nonequilibrium response

A fiequently-used approximation in modeling SD and other dynamical processes in hquids is that of linear response When apphed to SD it corresponds to assuming that nonequilibrium response of the system to the perturbation AE turned on at r = 0 can be approximated in terms of equilibrium fluctuations of AE in the absence of the perturbation, i.e., for the system con-taiiting the solvent and the ground-state (subscript 0) chromophore ... 

The dynamic (nonequilibrium) response of the solvent to the external field-induced oscillation in the solute electronic density (electronic nonequilibrium) has been formulated within the PCM in ref. [9], whereas vibrational nonequilibrium effects (due to the dynamics of the solvent resulting from solute vibrational motions) have been formulated, still within the PCM, in ref. [43],... 

Figure 3.15 Results of simulation of solvation dynamics of chromophore C153 in room-temperature acetonitrile via nonequilibrium and equilibrium MD simulation methods. SRF stands for solvation response function. In the notation used here neq is the nonequilibrium response S(t), ground is the equilibrium TCF C0(t) and excited is the equilibrium TCF C, (f). (Reprinted from F. Ingrosso, B. M. Ladanyi, B. Mennucci, M. D. Elola, and J. Tomasi, I. Phys. Chem. B, 109, 3553-3564. Copyright (2005), with permission from American Chemical Society).

Alternatively, one could use SLLOD equations to do direct simulations, such as shear a system under planar Couette flow and measure the shear stress. As we have already discussed, this approach has been used successfully to calculate a host of transport properties. It is important to remember, however, that direct simulation is often unable to simulate realistic materials at experimentally accessible shear rates. At low shear rates, the nonequilibrium response becomes small compared to the magnitude of the equilibrium fluctuations that naturally arise. The extremely small signal-to-noise ratio would demand prohibitively long simulations before any meaningful answers could be obtained. 

For a sufficiently weak external force F (r, t), the departure pt) = pt) - peq) from equilibrium is expected to be small. Then pt> peq>- Assuming t s to be the case, the nonequilibrium response function equilibrium response function... 

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... 

Arguably a more practical approach to higher-order nonequilibrium states lies in statistical mechanics rather than in thermodynamics. The time correlation function gives the linear response to a time-varying field, and this appears in computational terms the most useful methodology, even if it may lack the... 

Many solvents do not possess the simple structure that allows their effects to be modeled by the Langevin equation or generalized Langevin equation used earlier to calculate the TS trajectory [58, 111, 112]. Instead, they must be described in atomistic detail if their effects on the effective free energies (i.e., the time-independent properties) and the solvent response (i.e., the nonequilibrium or time-dependent properties) associated with the... 

A closer look at different methods helps us to understand which features are responsible for their success. Let us compare, for instance, the nonequilibrium work method with the adaptive equilibrium approaches, described above. In the most common implementation of the former, the instantaneous force acting on the system along the order parameter is always equal to zero. In contrast, in the adaptive... 

Nonequilibrium considerations for electron transfer are similar to those for vertical photoexcitation discussed above, except that the pre-organization of the solvent prior to the electron transition makes the effective gap at the time of the electron transfer smaller, and thus the assumption of rapid electronic response of the solvent is even better. 

Osmotic Work. It is characteristic of living cells that they maintain nonequilibrium values of the concentrations of certain solutes on opposite sides of membranes, particularly ions such as Na and K. It is this nonequHibrium distribution of ions that probably is responsible for the electrical potentials developed by living organisms. Again, although thermodynamic data do not lead to deductions about molecular mechanisms, they provide limiting values with which any mechanism must be consistent. We shall discuss the thermodynamic aspects of osmotic work in detail when we have developed the methods requited to deal with solutions. 

The time and temperature dependent properties of crosslinked polymers including epoxy resins (1-3) and rubber networks (4-7) have been studied in the past. Crosslinking has a strong effect on the glass transition temperature (Tg), on viscoelastic response, and on plastic deformation. Although experimental observations and empirical expressions have been made and proposed, respectively, progress has been slow in understanding the nonequilibrium mechanisms responsible for the time dependent behavior. 

The nonequilibrium glassy state, 5(t) = f(t) -f, is determined by solving the kinetic equations which describe the local motion of holes in response to molecular fluctuations during vitrification and physical aging. The solution is (11)... 

The world surrounding us is mostly out of equihbrium, equilibrium being just an idealization that requires specific conditions to be met in the laboratory. Even today we do not have a general theory about nonequilibrium macroscopic systems as we have for equilibrium ones. Onsager theory is probably the most successful attempt, albeit its domain of validity is restricted to the linear response regime. In small systems the situation seems to be the opposite. Over the past years, a set of theoretical results that go under the name of fluctuation theorems have been unveiled. These theorems make specific predictions about energy processes in small systems that can be scrutinized in the laboratory. 

---