New-sprung emphasis on the continuum approach does not mean that processes operating at sub-REV scales have been ignored. Indeed it is these phenomena that determine the properties of the continuums, and there is an emerging need to characterize links between kinetic processes that operate on disparate scales as fluid flows through reactive rock [ Torgersen, 1994].
The exchange of energy between reactive metamorphic rock and flowing fluid has generally been accounted for by adjusting heat capacities to accommodate heats of reaction (or some equivalent formalism). While rates of irreversible processes have been included in this approach, the energetics of irreversibility have not because rates and coupled heat capacities alone do not provide for irreversible interconvertibility among chemical, mechanical, and thermal energy. Given that real processes are irreversible, is this preterition severe?
Nonequilibrium thermodynamics suggests that entropy might be a useful device for assessing the importance of coupling of small-scale irreversibility (intra-REV or intrasystem phenomena) and larger scale metamorphic fluid flow (inter-REV phenomena).
The time (t) evolution of the entropy (S) of
an evolving rock REV is composed of a net flow term 
and a production term 
:
Entropy flow results from temperature-normalized heat and material flows through the system. It depicts the energy associated with larger scale, inter-REV processes such as fluid flow. Entropy production is a positive definite sum of fluxes multiplied by forces that drive them. It includes intra-REV force-flux products arising from reaction kinetics, mass transfer, heat transfer, and viscous flow that occur at small (e.g., microscopic) scales. The time rate of change in REV entropy is thus seen to depend on both macroscopic and microscopic processes.
Recent work by Carlson and Denison [1992] and Denison and Carlson [1993] underscores the importance of integrating all scales of observation. Using high-resolution X ray tomography to quantify the disposition and size of mineral grains at the millimeter scale, Carlson and Denison showed that porphyroblast growth rates are controlled by intergranular chemical diffusion in a variety of metamorphic rocks, including calcsilicate skarn affected by coeval fluid infiltration. In the case of the skarn, the results imply that rates of intergranular diffusion exceeded fluid pore velocities. Having documented the prevalence of irreversible (i.e., real) diffusive mass transfer in rock during metamorphic fluid flow by virtue of its rate-limiting character, we are now impelled to consider the energetics of the process. Entropy flow and production can be used for this purpose.
Consider the case of entropic steady state where 
. The entropy budget for irreversible diffusion of
species i at constant temperature yields the conservation relation
where 
has been written in terms of temperature
T and heat flux 
(
is corrected for heat
contributed by flowing material), 
is the chemical potential
of diffusing component i, and 
is the molar diffusive
flux of component i. The equation shows that entropy production by
irreversible chemical diffusion (right-hand side) can, in principle,
influence net heat flux (left-hand side) during metamorphism. Since
local entropy production by diffusion is positive, so is the
associated change in heat flux. Some of this thermal
energy was advected by flowing fluid in the case of the skarn.
Data needed to evaluate such couplings are scant at present. However, estimates for diffusive flux and chemical potential gradients summarized by Joesten [1991] indicate that the amount of thermal energy liberated by diffusion could be substantial (e.g., commensurate with heats of reaction).
How do irreversible processes like diffusive mass transfer influence
thermal budgets when integrated over entire fluid flow systems? How
does the presence or absence of fluid affect 
? At what scales,
from micrometer to kilometer, might we expect to see manifestations
of such effects? Answers to these and similar questions should be
forthcoming as the mutual influences of hydrodynamics and geochemical
reactions are explored over a wide range of scales by workers in the
field, in the laboratory, and in the realm of numerical models.