A thermodynamic description of liquid flows in capillaries with hydrodynamic slip at the solid-liquid interface is given. Slip over the capillary wall brings into play surface interactions and therefore involves interfacial energy and entropy. Energy and entropy balance equations are written so as to take into account surface effects. The two relations constitute a general mathematical model that allows readily analyzing various situations and to explore the behavior of such thermodynamic process. The main result derived concerns the existence of a capillary pressure of slip; slip occurrence leads to a pressure decrease in the flow and might cause cavitation. The variation in magnitude of the slip effect, viewed as a thermodynamic transformation, may take place irreversibly. Slip irreversibility and the probable occurrence of a two-phase flow regime are possible factors that may cause additional pressure drop. (C) 2010 American Institute of Chemical Engineers AIChE J, 57: 2251-2263, 2011