What to worry about

During simulation, the system has to have enough time to wander through all parts of the phase space that are accessible in the experimental conditions (with which the simulation is to be compared). We are never sure that it happens. We have to check whether the computed mean values depend upon the simulation time. If they do not, then very probably everything is all right - we have a description of the equilibrium state. 

The results of the MD (the mean values) should not depend on the starting point, because it has been chosen arbitrarily. This is usually satisfied for small molecules and their collections. For large and flexible molecules we usually start 

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