System size and geometry

The argument that even the most powerful digital computer cannot compute the potential energy of a system with macroscopic dimensions was already discussed in the first chapter. It is not feasible to determine properties of Avogadro s number of particles. Thankfully, it is also unnecessary. 

The fluctuations of thermodynamic properties computed from microscopic systems of size N scale as (VA) With N = 10000 particles, the standard deviation of a macroscopic state function is already 1% of the property value. Currently, simulations can be routinely conducted with O(IO ) particles, often reaching O(IO ) particles, decreasing the error to insignificant levels. Consequently, if adequate sampling of the phase space points is numerically generated, the properties can be accurately determined even if the phase space is of a significantly smaller system than a bulk one. 

Practically, a system as large as is affordable should be simulated. Traditionally, limitations have been associated with the size of available computer memory. Storing the Cartesian positions, velocities, accelerations, and forces of a system with A = 10 requires approximately 100 MB of random access memory (RAM). The RAM is needed as opposed to hard drive space because during a simulation accessing these numbers from a hard drive would be prohibitively slow. Only high-end computers had such large RAM available until the 1990s. Currently 

Of consideration remains the actual wall-clock time required in order to generate a sufficiently large sample of microscopic states. We discuss the time-related considerations separately for Monte Carlo and molecular dynamics simulations in the next two chapters. 

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