  In this article, we continue the program started in our previous article of
exploring an important class of thermodynamic systems from a geometric point of
view. In order to model the time evolution of systems verifying the two laws of
thermodynamics, we show that the notion of evolution vector field is adequate
to appropriately describe such systems. Our formulation naturally arises from
the introduction of a skew-symmetric bracket to which numerical methods based
on discrete gradients fit nicely. Moreover, we study the corresponding
Lagrangian and Hamiltonian formalism, discussing the fundamental principles
from which the equations are derived. An important class of systems that is
naturally covered by our formalism are composed thermodynamic systems, which
are described by at least two thermal variables and exchange heat between its
components.}.
