Nonequilibrium approaches free energy calculations

De Koning, M., Optimizing the driving function for nonequilibrium free-energy calculations in the linear regime. A variational approach, J. Chem. Phys. 2005, 122,... 

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. 

There have been many applications of the nonequilibrium free energy calculations in the literature, and here we outline a number of them. The Crooks FR has been using in simulations and experiments, but presumably because of the simplicity of evaluation of the free energy using JE, this relationship is much more widely used. In some particular examples, advantages of the Crooks approach have been noted. 

As we will see further in the book, almost all methods for calculating free energies in chemical and biological problems by means of computer simulations of equilibrium systems rely on one of the three approaches that we have just outlined, or on their possible combination. These methods can be applied not only in the context of the canonical ensemble, but also in other ensembles. As will be discussed in Chap. 5, AA can be also estimated from nonequilibrium simulations, to such extent that FEP and TI methods can be considered as limiting cases of this approach. 

In natural waters organisms and their abiotic environment are interrelated and interact upon each other. Such ecological systems are never in equilibrium because of the continuous input of solar energy (photosynthesis) necessary to maintain life. Free energy concepts can only describe the thermodynamically stable state and characterize the direction and extent of processes that are approaching equilibrium. Discrepancies between predicted equilibrium calculations and the available data of the real systems give valuable insight into those cases where chemical reactions are not understood sufficiently, where nonequilibrium conditions prevail, or where the analytical data are not sufficiently accurate or specific. Such discrepancies thus provide an incentive for future research and the development of more refined models. 

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