Non-equilibrium thermodynamics increasingly has very wide application in many fields of science and engineering but apart from a flurry of activity in the 1960's to 1980's there has been relatively little application within geology. Recently there has been a resurgence of interest in non-equilibrium thermodynamics with respect to damage mechanics and to seismology, and in structural geology/geodynamics. We set out here to discuss some important applications of non-equilibrium thermodynamics to deforming, reacting metamorphic systems. We make a distinction between classical chemical thermodynamics where minimisation of the Gibbs Free Energy defines the stable states and non-equilibrium thermodynamics where either minimisation or maximisation of the entropy production rate defines the stable phases.
The problem in applying non-equilibrium thermodynamics to geological problems derives from the apparent lack of a set of guiding principles that would allow progress. In any system, whether at equilibrium or not, one can define a function, the Gibbs Free Energy. This function is minimised at equilibrium and so one can proceed to define equilibrium assemblages of minerals. Another function, the entropy, is maximised at equilibrium. For non-equilibrium systems, it has never been clear, until recently, that a similar principle was available. In fact, two apparently opposing views seemed to emerge in the literature. One is due to Prigogine (1955) who claimed that in non-equilibrium systems, the rate of entropy production is minimised. The other view is due to Zeigler (1980) who claimed that the rate of entropy production is maximised in non-equilibrium systems. This apparent paradox is resolved when one understands that the Prigogine principle holds for linear steady state systems whereas the Zeigler principle holds for systems that are not constrained to be at steady state. This now opens the way to describe the evolution of geological systems that are forced out of equilibrium by continued deformation, fluid flow, heat flow and chemical reactions.
Metamorphism is commonly associated with deformation and regional thermal gradients, together with chemical reactions, all of which are non-equilibrium situations. In many instances, especially at low metamorphic grades, another non-equilibrium process, namely fluid flow, accompanies the metamorphic process and is intimately coupled to deformation, heat advection and chemical reactions. We explore the influence of energy dissipated by such processes upon the structures and metamorphic assemblages and microstructures commonly observed in deformed metamorphic rocks.
To focus the discussion we concentrate on metamorphic rocks undergoing only deformation and chemical reactions and exclude the effects of fluid transport.