A classical virial theorem for open systems

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Abstract
A generalized classical virial equation is derived, superior to the equations already existing in three respects: (i) applicability to assemblies of fluctuating numbers of particles; (ii) applicability to assemblies subjected to net external action; (iii) applicability to any arbitrarily selected part of a larger assembly. It is found that the momentum in- and out-flux densities, caused by particles crossing the limiting surfaces, contribute to the virial. The equation is applied to a homogeneous gas, and the ideal gas law is derived. Invariance criteria are studied, and translations and division into subsystems are discussed. Various internal and external contributions to the virial are discussed and compared for the new and the already existing virial equations.
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