Pressure and equilibrium in deforming rocks

It is widely proposed that tectonic pressure (the difference between the mean stress and the pressure arising from a lithostatic load) is large, and has a significant influence on mineral phase equilibria in deforming metamorphic rocks. The implication/assertion is that the mean stress is equivalent to the thermodynamic pressure which characterizes mineral phase equilibria and is a measure of how the energy changes as the volume changes. We distinguish two useful thermodynamic pressures. The first is an equilibrium thermodynamic pressure, characteristic of non-dissipative systems and related directly to equilibrium values of the chemical potentials that define stable, equilibrium phase assemblages. The second is a non-equilibrium thermodynamic pressure characteristic of dissipative systems with zero net entropy production and related to non-equilibrium chemical potentials that define stable non-equilibrium phase assemblages. In many dissipative metamorphic systems discussed in the literature, the concepts of thermodynamic pressure and chemical potential are not usefully defined because the system is not at equilibrium and/or no volume change is involved in the deformation. The conclusion of this note is that the influence of tectonic pressure on phase equilibria is minor. The role of tectonic pressure is an important issue but is only relevant to phase equilibrium when an equilibrium thermodynamic pressure can be defined; in such cases, the influence of tectonic pressure is small compared to many proposals in the literature. Except for elastic deformations, the mean stress is not useful in discussing mineral phase equilibrium.