Two World Views of Entropy Production: Application to Understanding Soil Structure Formation and Dual-Flow Networks.

Classical sciences have relied heavily on the first law of thermodynamics (i.e., energy conservation), while the second law of thermodynamics (i.e., energy change or evolution) has not yet made significant inroads. Entropy, the central concept of the second law, is a unique physical quantity that tends towards maximum over time in the universe.  It meters irreversibility that is characteristic of complex natural processes.  The total change of entropy for an open system (dS_total) can be partitioned into (1) the entropy produced inside the system (d_iS) and (2) the entropy transferred across the system boundaries (d_eS = S_in – S_out). Two contrasting entropy production principles are identified: (1) statistical entropy associated with a random world, where d_iS is maximized (i.e., maximum entropy production) leading to maximum randomness and least biased distribution inside a system that is towards equilibrium; and (2) energetic entropy associated with a structured world, where d_eS is maximized (i.e., maximum entropy export) leading to a maximum organization inside a system that is far from equilibrium. These entropy principles can be used to explain the simultaneous occurrence of dissipation (forming soil matrix) and organization (forming soil structure) during pedogenesis. This is consistent with Prigogine’s dissipative structure concept and self-organization principle. There are three possibilities for the entropy balance in a soil system: (1) dS_total/dt > 0, (2) dS_total/dt < 0, or (3) dS_total/dt = 0, where t is time.  In the first case, the soil loses order; in the second case, the soil gains order; and in the third case, the soil is in stationary or steady-state.  For a soil to further develop its structure and/or remain ordered, dS_total/dt must be ≤ 0.  This is only possible if –d_eS ≥ d_iS ≥ 0.  Most soils formed in nature are progressively more ordered than their precursors, thus suggesting that the maximum entropy export principle should have been at work during pedogenesis.  This results in ubiquitous structured heterogeneity in natural soils that leads to widespread dual-flow regimes (i.e., fast preferential flow and slow matrix flow), which form the basis for subsurface flow networks. The entropy principles offer a unique thermodynamic perspective on the interactions between natural soils and their surrounding environments and the development of internal architecture in soils and its impacts on flow regimes.