Entropy sampling methods

Another class of methods that has been used to remove sampling difficulties is based on what is often called the multicanonical ensemble These methods have also been called entropy sampling methods,for reasons that are made clear below. It is easiest to understand the multicanonical methods by considering the full classical canonical coordinate-momentum distribution... 

A novel approach to protein conformation is the entropy-sampling Monte Carlo method (ESMC), which is described in detail in another contribution to this volume. The method provides a complete thermodynamic description of protein models, but it is computationally quite expensive. However, because of the underlying data-parallel structure of ESMC algorithms, computations could be done on massively parallel computers essentially without the communication overhead typical for the majority of other simulation techniques. This technique will undoubtedly be applied to numerous systems in the near future. 

The first NUS approaches have used experimentally weighted random sampling methods and variations of random sampling. However, other NUS methods, such as radial sampling with projection reconstruction, have been proposed (see introduction). Different algorithms have been used for reconstruction of NUS data, such as Maximum Entropy or Maximum Likelihood Methods. It is beyond the scope of this chapter to compare exhaustively the different approaches. Here we use just the FM reconstruction software to compare the performance of different random sampling schedules where the randomness is skewed by weighting functions. 

In Chapter 4, it has already been stated that it is an advantage of the simple-sampling algorithms based on Rosenbluth sampling [33], compared to importance-sampling methods, that they allow for the approximation of the degeneracy ( density ) of states absolutely, i.e., free energy and entropy can be explicitly determined. 

To calculate canonical averages of an observable f x,p) using the entropy distribution (Eq. [47]), we can implement umbrella sampling methods... 

What has been developed within the last 20 years is the computation of thermodynamic properties including free energy and entropy [12, 13, 14]. But the ground work for free energy perturbation was done by Valleau and Torrie in 1977 [15], for particle insertion by Widom in 1963 and 1982 [16, 17] and for umbrella sampling by Torrie and Valleau in 1974 and 1977 [18, 19]. These methods were primarily developed for use with Monte Carlo simulations continuous thermodynamic integration in MD was first described in 1986 [20]. 

The simplest method to measure gas solubilities is what we will call the stoichiometric technique. It can be done either at constant pressure or with a constant volume of gas. For the constant pressure technique, a given mass of IL is brought into contact with the gas at a fixed pressure. The liquid is stirred vigorously to enhance mass transfer and to allow approach to equilibrium. The total volume of gas delivered to the system (minus the vapor space) is used to determine the solubility. If the experiments are performed at pressures sufficiently high that the ideal gas law does not apply, then accurate equations of state can be employed to convert the volume of gas into moles. For the constant volume technique, a loiown volume of gas is brought into contact with the stirred ionic liquid sample. Once equilibrium is reached, the pressure is noted, and the solubility is determined as before. The effect of temperature (and thus enthalpies and entropies) can be determined by repetition of the experiment at multiple temperatures. 

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