Significance The stability of Poiseuille flow is among the most classical problems in fluid mechanics going back to the pioneering work of Reynolds. Despite a huge amount of effort, particularly recent advances in experimental studies, we still lack a suitable theoretical framework. In this paper, we develop a thermodynamic formalism for studying this problem. We show that this formalism allows us to identify a unique critical Reynolds number at which the laminar flow loses stability. We also study the free energy, action, and other thermodynamic relations for the macroscopic quantities associated with the flow. The formalism developed here should be applicable to a large class of problems exhibiting subcritical instabilities.