Physical Modeling of the Free Energy of Soil Water in Adequacy with the Carnot Cycle and Clausius Inequality

In classical thermodynamics, entropy (S) and temperature (T) are two associated thermodynamic variables whose dimensional equations are unknown but whose product (TS) is, like heat (Q), an energy (ML2T-2). This poses an unsurpassable barrier in form of an "thermodynamic 2nd law" when one wants to deepen the soil and water thermodynamic interaction and take into account the hierarchically organized structure in aggregates of the solid phase. This problem has recently evolved with what has been called “systemic soil water thermodynamics” where all thermodynamic variables had to be “systemic” to fit into the “physical and systemic modeling” paradigm of Hydrostructural Pedology. With their dimensional identity, all the thermodynamic variables, being systemic, appear at the different organizational levels of a soil horizon, including those, molecular and atomic, of the fluid phases of the pedostructure. With this new point of view, the Carnot cycle explicitly confirms the correspondence between the traditional thermodynamic terminology and the systemic variables and equations of the new thermodynamics model. However, a completely different interpretation of the Carnot cycle and the Clausius inequality is highlighted here, one that has nothing to do with the question of reversibility/irreversibility but rather with the fundamental physical process at the basis of the thermodynamic equilibrium and its evolving with time. The Clausius inequality is explained and new fields of research are emerging in perspective.