  We discuss the relevance of geometric concepts in the theory of stochastic
differential equations for applications to the theory of non-equilibrium
thermodynamics of small systems. In particular, we show how the
Eells-Elworthy-Malliavin covariant construction of the Wiener process on a
Riemann manifold provides a physically transparent formulation of optimal
control problems of finite-time thermodynamic transitions. Based on this
formulation, we turn to an evaluative discussion of recent results on optimal
thermodynamic control and their interpretation.
