Configuration space, equilibrium phase thermodynamics

Figure 1 Schematic behavior of the function f-AE) = v( )exp[—E/ gT] at a finite temperature T (see discussion about Eqs. [13]-[16]). For a large system, /ij.( ) has a sharp peak at the typical energy , and v( ) is very small, which means that the part of configurational space contributing significantly to this function is exceedingly small. In the case of a first-order phase transition, two peaks exist. A peptide can reside in several different stable states in thermodynamic equilibrium corresponding to several peaks of / j.( ) however because of the relatively small system size, the maxima of f (E) will not be sharp (compare with Figure 2).

A sequence of successive configurations from a Monte Carlo simulation constitutes a trajectory in phase space with HyperChem, this trajectory may be saved and played back in the same way as a dynamics trajectory. With appropriate choices of setup parameters, the Monte Carlo method may achieve equilibration more rapidly than molecular dynamics. For some systems, then, Monte Carlo provides a more direct route to equilibrium structural and thermodynamic properties. However, these calculations can be quite long, depending upon the system studied. 

The small number of variables needed for thermodynamic state description is certainly surprising from a microscopic molecular dynamic viewpoint. For the complete molecular-level description of an arbitrary state (phase-space configuration) of the order of 1023 particles, we should expect to require an enormously complex nonequilibrium function independent variables (i.e., positions rt and velocities r,-), time evolution until equilibrium is achieved, we find that a vastly simpler description is possible for the resulting equilibrium state state properties R, R2.i.e., for a pure substance,... 

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