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Postulate 1: Ergodic Hypothesis: Given enough time, a system will sample all microstates consistent with the constraints imposed. That is, time averages are equivalent to ensemble averages. Mathematically, we have xii 1 X i lim xiti (3.7) where i is the probability density of state i. Postulate 2: Equal a Priori Probabilities: All microstates having the same energy are equally probable. Mathematically, i i(Ei) (3.8) 3.2.3 Ensembles Ensembles are classified according to the constraints imposed on the corresponding thermodynamic system. The four most important types are the microcanonical ensemble NVE, the canonical ensemble NVT, isothermal-isobaric NPT and the grand canonical ensemble μVT. The microcanonical ensemble is the assembly of all states with fixed total energy E, and fixed size, usually specified by the number of molecules, N, and volume V. Such a system cannot exchange either matter or energy with its surroundings. Neither can it expand or contract in volume. The canonical ensemble corresponds to an assembly of all microstates with fixed N and V. The energy can fluctuate; however, the system is kept at equilibrium by being in contact with a heat bath. The canonical ensemble, in which the temperature, number of molecules and volume are imposed, is used for monophasic fluids when density is known. The predicted average properties are then average energy, pressure and chemical potential. In the isothermal-isobaric or NPT ensemble, pressure is imposed instead of volume of the system. Usually, NPT is used to predict fluid density. This ensemble is 36 i xt i iPDF Image | MOLECULAR SIMULATION STUDIES IN THE SUPERCRITICAL REGION
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