Two very different sorts of experiments have characterized the field of cardiac energetics over the past three decades. In one of these, Gibbs and colleagues measured the heat production of isolated papillary muscles undergoing isometric contractions and afterloaded isotonic contractions. The former generated roughly linear heat vs. force relationships. The latter generated enthalpy-load relationships, the peak values of which occurred at or near peak isometric force, i.e., at a relative load of unity. Contractile efficiency showed a pronounced dependence on afterload. By contrast, Suga and coworkers measured the oxygen consumption (V̇o₂) while recording the pressure-volume-time work loops of blood-perfused isolated dog hearts. From the associated (linear) end-systolic pressure-volume relations they derived a quantity labeled pressure-volume area (PVA), consisting of the sum of pressure-volume work and unspent elastic energy and showed that this was linearly correlated with V̇o₂over a wide range of conditions. This linear dependence imposed isoefficiency: constant contractile efficiency independent of afterload. Neither these data nor those of Gibbs and colleagues are in dispute. Nevertheless, despite numerous attempts over the years, no demonstration of either compatibility or incompatibility of these disparate characterizations of cardiac energetics has been forthcoming. We demonstrate that compatibility between the two formulations is thwarted by the concept of isoefficiency, the thermodynamic basis of which we show to be untenable.