## Section: Application Domains

### Chemistry

The treatment of *chemical reactions* in the framework of OT is a rather recent development.
The classical theory must be extended to deal with
the transfer of mass between different particle species by means of chemical reactions.

A promising and significant recent advance is the introduction and analysis of a novel metric
that combines the pure transport elements of the Wasserstein distance
with the annihilation and creation of mass, which is a first approximation of chemical reactions.
The logical next challenge is the extension of OT concepts to vectorial quantities,
which allows to rewrite cross-diffusion systems for the concentration of several chemical species as gradient flows in the associated metric.
An example of application is the modeling of a *chemical vapor deposition process*,
used for the manufacturing of thin-film solar cells for instance.
This leads to a degenerate cross-diffusion equations, whose analysis — without the use of OT theory — is delicate.
Finding an appropriate OT framework to give the formal gradient flow structure a rigorous meaning
would be a significant advance for the applicability of the theory, also in other contexts, like for biological multi-species diffusion.

A very different application of OT in chemistry is a novel approach to the understanding of *density functional theory* (DFT)
by using optimal transport with “Coulomb costs”, which is highly non convex and singular.
Albeit this theory shares some properties with the usual optimal transportation problems,
it does not induce a metric between probability measures.
It also uses the multi-marginal extension of OT, which is an active field on its own right.