The Clausius inequality is converted to an equality in which a positive quantity with units of energy, termed the deficit function, is used to track entropy production and other effects of irreversible processes. This inequality rectification procedure is shown to yield particularly transparent new derivations of several important results based on the Second Law, with some consequences that have apparently not been previously recognized. For example, the Helmholtz free energy of any system is shown to decrease towards a minimum as the result of any spontaneous processes which begin and end at the same temperature and involve no work exchange, without the need to invoke the stricter requirements of fixed system volume and/or chemical composition. (C) 2003 American Institute of Physics.