  We investigate the consequences of reparametrizations in the geometric
description of thermodynamics analyzing the effects on the thermodynamic phase
space. It is known that the contact and Riemannian structures of the
thermodynamic phase space are related to thermodynamic equilibrium and
statistical fluctuations in the Boltzmann-Gibbs statistical mechanics. The
physical motivation for this analysis rests upon the possibility of having,
instead of a direct control of the intensive parameters determining the state
of the corresponding physical reservoirs, the control of a set of
differentiable functions of the original variables. Likewise, we consider a set
of differentiable functions of the extensive variables accounting for the
possibility of not having direct access to the original variables. We find that
the effect of reparametrizations on the thermodynamic phase space can be
codified, in geometrical terms, in its contact and Riemannian structures. In
particular, we single out a rank-two tensor that enters in the definition of
the metric which geometrically comprises the information about such
reparametrizations. We notice that even if these geometric structures are
modified by the reparametrizations, the metric structure on the thermodynamic
space of equilibrium states is preserved.
