  Depending on context, the term entropy is used for a thermodynamic quantity,
a~measure of available choice, a quantity to measure information, or, in the
context of statistical inference, a maximum configuration predictor. For
systems in equilibrium or processes without memory, the mathematical expression
for these different concepts of entropy appears to be the so-called
Boltzmann--Gibbs--Shannon entropy, H.For processes with memory, such as driven-
or self-reinforcing-processes, this is no longer true: the different entropy
concepts lead to distinct functionals that generally differ from H. Here we
focus on the maximum configuration entropy (that predicts empirical
distribution functions) in the context of driven dissipative systems. We
develop the corresponding framework and derive the entropy functional that
describes the distribution of observable states as a function of the details of
the driving process. We do this for sample space reducing (SSR) processes,
which provide an analytically tractable model for driven dissipative systems
with controllable driving. The fact that a consistent framework for a maximum
configuration entropy exists for arbitrarily driven non-equilibrium systems
opens the possibility of deriving a full statistical theory of driven
dissipative systems of this kind. This provides us with the technical means
needed~to derive a thermodynamic theory of driven processes based on a
statistical theory. We discuss the Legendre structure for driven systems.
