Geometry and control of thermodynamic systems described by generalized exponential families

In this paper we investigate the geometric structure and control of exponential families depending on additional parameters, called external parameters. These generalized emerge naturally when one applies maximum entropy formalism to derive equilibrium statistical mechanics framework. We study associated model, compute Fisher metric introduce a natural fibration parameter space over space. The Riemannian allows endow with an Ehresmann connection geometry these models. As example, show that horizontal lift paths in corresponds isentropic evolution system. apply theory example ideal gas rotating rigid container.