Thermodynamic optimization - Equipartition of entropy production

Remember that the second principle of thermodynamics stipulates that in any real, irreversible process, net entropy production is positive. This quantity, expressed in joules per kelvin (or in $W\cdot K^{-1}$ if it is a power), is therefore a natural and general measure of the irreversibility of a process. When it comes to the irreversibility of purely thermal phenomena, entropy is the only appropriate thermodynamic function, as it is the extensive quantity "conjugated" to the intensive quantity temperature. In certain other cases, other quantities can play this role, in particular energetic quantities, therefore expressed in J or W, such as viscous dissipation in flows, or dissipation by the Joule effect in electricity, or the heat released by an irreversible chemical reaction. In all these cases, we're actually measuring a quantity of heat generated by the irreversible degradation of a noble form of energy (mechanical or electrical or chemical in these examples). It is always possible, but not necessary, to reduce to entropy by dividing this generated thermal energy by a suitably chosen reference temperature. Exergy is also a quantity that is homogeneous with energy, and whose destruction is a measure of irreversibility. We'll devote a few pages to recalling and clarifying the relationship between this quantity and the production of entropy.

We are therefore interested in processes and systems that are not ideal in the sense of reversibility. We intuitively understand that irreversibilities are "bad" for performance, as they degrade a form of energy, and so we always seek, explicitly or implicitly, to minimize them. The problem is that if certain precautions are not taken, this minimization leads to completely unrealistic process dimensioning and/or operating conditions that are devoid of any practical interest, such as transfer surface dimensions that become very large, or extremely slow process speeds. Taking precautions here means ensuring that all physical quantities are finite, and that the useful tasks expected of the process are carried out correctly. This approach defines what we now call "finite-time or finite-dimension thermodynamics", or finite-task thermodynamics (§ 1).

The thermodynamics of irreversible processes offers a rigorous, if not convenient, framework for expressing and studying entropy production, particularly in its linear version, where flows (of matter, electricity, momentum, thermal energy) are affine functions of driving forces (gradients of chemical potential, electrical potential, velocity, inverse temperature). Most of the time, we will use this linear framework to establish...