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It is rarely the case that the starting conditions of a simulation (the particle coordinates and velocities) correspond to a configuration that is consistent with the equilibrium distribution of the system. Often, in the construction of the system, an optimization of the geometry with respect to a forcefield has been performed in order to remove unphysical interactions, but this has the consequence of placing the system in a configuration that is a potential minimum.

If particle velocities are assigned at random from a Maxwell-Boltzmann distribution and an integration is then performed in the microcanonical ensemble (i.e. internal energy is conserved), a decline in temperature is observed as some of the kinetic energy is transferred to potential energy. It is thus important that the simulation is run for a period before any analysis is conducted, in order to ensure that it is properly at equilibrium. In many cases the equilibrium can be facilitated by the application of a thermostat.

There are a number of methods for determining when a system is at equilibrium: approximate methods include plotting the energy or temperature against time, at equilibrium these quantities will fluctuate around constant averages. More sophisticated methods include calculating order parameters (see Allen and Tildesley, 1987).
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