The widely held view that the maximum efficiency of a photosynthetic pigment system is given by the Carnot cycle expression (1-T/Tr) for energy transfer from a hot bath (radiation at temperature Tr) to a cold bath (pigment system at temperature T) is critically examined and demonstrated to be inaccurate when the entropy changes associated with the microscopic process of photon absorption and photochemistry at the level of single photosystems are considered. This is because entropy losses due to excited state generation and relaxation are extremely small (DeltaS 0.98 and xi > 0.92 respectively, and which, in principle, function with negative entropy production. It is demonstrated that for the case of xi > (1-T/Tr) entropy production is always negative and only becomes positive when xi < (1-T/Tr).