  In this paper, a formalism for the activation volume of glass forming
materials is suggested. An isothermal equation of state for the activation
volume is formulated, which is extended to a generalized equation of state that
describes the activation volume as a function of temperature and pressure. Both
the equations of state are very successfully validated by using experimental
and simulation data collected for supercooled Kob-Andersen binary Lennard-Jones
liquid and materials from various material groups such as van der Waals
liquids, polymers, protic ionic liquids, and strongly hydrogen bonded liquids.
Some predictions based on these equations of state for the activation volume
are also very satisfactorily verified in case of each considered system,
especially a kind of the activation volume scaling with the scaling exponent
that also constitutes the slope of the expected linear pressure dependence of
the isothermal bulk modulus for the activation volume is confirmed. The until
recently unexpected negative value of the slope are explained in case of the
systems that obey the thermodynamic scaling law at least to a good
approximation.
