Virial pressure

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The virial pressure is commonly used to obtain the pressure from a general simulation. It is particularly well suited to molecular dynamics, since forces are evaluated and readily available. For central interactions, one has:

 p  =  \frac{ k_B T  N}{V} - \frac{ 1 }{ d V } \overline{ \sum_{i<j} {\mathbf f}_{ij}  {\mathbf r}_{ij} },

where one can recognize an ideal term, and a second term due to the virial. The overline is an average, which would be a time average in molecular dynamics, or an ensemble average in Monte Carlo; d is the dimension of the system (3 in the "real" world).  {\mathbf f}_{ij} is the force on particle i exerted by particle j, and {\mathbf r}_{ij} is the vector going from i to j: {\mathbf r}_{ij} = {\mathbf r}_j - {\mathbf r}_i.