Stochastic thermodynamics for "Maxwell demon" feedbacks

We propose a way to incorporate the effect of a specific class of feedback processes into stochastic thermodynamics. These "Maxwell demon" feedbacks do not affect the system energetics but only the energy barriers between the system states (in a way which depends on the system states). They are thus of a purely informational nature. We show that the resulting formalism can be applied to study the thermodynamic effect of a feedback process acting on electron transfers through a junction.