Contraction of the heart is caused by actin filaments sliding along myosin filaments. This generates a frictional force inducing wear of the contractile apparatus. We postulated that this process could be exacerbated when the heart was submitted to severe anoxia. Anoxia induced dramatic abnormalities in the molecular properties of actin-myosin crossbridges. We applied the formalism of far-from-equilibrium thermodynamics to the left ventricular papillary muscles (LVPMs) of mammalian rat hearts which had been subjected to a prolonged anoxia (3 h). We showed that when subjected to prolonged anoxia, the heart operated far-from-equilibrium as evidenced by the non-linearity between thermodynamic force (F/T: Frictional force/Kelvin temperature) and thermodynamic flow (v0: myofilament sliding velocity). The rate of entropy production (EPR) was the product of (F/T) and v0. The excess entropy production (EEP) was equal to = vo; (S: entropy). The tribological system remained stable when EEP was positive and became unstable when EEP became negative, thus characterizing instability of the system and reflecting the occurrence of self-organization and possibly dissipative structures. After 3 h anoxia, re-oxygenation induced significant reversibility. About 20% of the myosin heads did not recover despite re-oxygenation. These results may be of importance in the context of heart transplantation where the delay between the time of sampling from the donor and the time of the graft installation in the recipient should be as short as possible.