Entropy production

Entropy production determines the performance of thermal machines such as power plants, heat engines, refrigerators, heat pumps, and air conditioners. It also plays a key role in the thermodynamics of irreversible processes.

Entropy is produced in irreversible processes. The importance of avoiding irreversible processes (hence reducing the entropy production) was recognized as early as 1824 by Carnot. In 1867 Rudolf Clausius expanded his previous work from 1854 on the concept of “unkompensierte Verwandlungen” (uncompensated transformations), which, in our modern nomenclature, would be called the entropy production. In the same article in which he introduced the name entropy, Clausius gives the expression for the entropy production (for a closed system), which he denotes by N, in equation (71) which reads

Here S is the entropy in the final state and the integral is to be taken from the initial state to the final state. From the context it is clear that N = 0 if the process is reversible and N > 0 in case of an irreversible process.

The laws of thermodynamics system apply to well-defined systems. Fig.1 is a general representation of a thermodynamic system. We consider systems which, in general, are inhomogeneous. Heat and mass are transferred across the boundaries (nonadiabatic, open systems), and the boundaries are moving (usually through pistons). In our formulation we assume that heat and mass transfer and volume changes take place only separately at well-defined regions of the system boundary. The expression, given here, are not the most general formulations of the first and second law. E.g. kinetic energy and potential energy terms are missing and exchange of matter by diffusion is excluded.

The rate of entropy production, denoted by ${\displaystyle {\dot {S}}_{i}}$, is a key element of the second law of thermodynamics for open inhomogeneous systems which reads

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