  The Thermodynamic Formalism provides a rigorous mathematical framework to
study quantitative and qualitative aspects of dynamical systems. At its core
there is a variational principle corresponding, in its simplest form, to the
Maximum Entropy principle. It is used as a statistical inference procedure to
represent, by specific probability measures (Gibbs measures), the collective
behaviour of complex systems. This framework has found applications in
different domains of science. In particular, it has been fruitful and
influential in neurosciences. In this article, we review how the Thermodynamic
Formalism can be exploited in the field of theoretical neuroscience, as a
conceptual and operational tool, to link the dynamics of interacting neurons
and the statistics of action potentials from either experimental data or
mathematical models. We comment on perspectives and open problems in
theoretical neuroscience that could be addressed within this formalism.
