  Thermodynamic macro variables, such as the temperature or volume macro
variable, can take on a continuum of allowable values, called thermodynamic
macro values. Although referring to the same macro phenomena, the macro
variables of Boltzmannian Statistical Mechanics (BSM) differ from thermodynamic
macro variables in an important respect: within the framework of Boltzmannian
Statistical Mechanics the evolution of macro values of systems with finite
available phase space is invariably modelled as discontinuous, due to the
method of partitioning phase space into macro regions with sharp, fixed
boundaries. Conceptually, this is at odds with the continuous evolution of
macro values as described by thermodynamics, as well as with the continuous
evolution of the micro state assumed in BSM. This discrepancy I call the
discontinuity problem (DP). I show how it arises from BSM's framework and
demonstrate its consequences, in particular for the foundational project of
reducing thermodynamics to BSM: thermodynamic macro values are shown to not
supervene on the corresponding BSM macro values. With supervenience being a
conditio sine qua non for the kind of reduction envisaged by the foundational
project, the latter is in jeopardy.
