Abstract
While optimality principles have been successfully used in many different areas related to flow processes in geosystems, their thermodynamic base has not been fully established. As an attempt to address this important issue, this chapter presents a thermodynamic hypothesis regarding optimality principles for the flow process. It states that a nonlinear natural system that is not isolated and involves positive feedbacks tends to minimize its resistance to the flow process that is imposed by its environment. Consistence between the hypothesis and typical flow processes in geosystems is demonstrated. In spirit, the hypothesis is consistent with Darwin’s evolution theory. It reconciles the seeming inconsistency between the minimization of energy expenditure rate principle and the maximum entropy production principle. An application of the hypothesis to calculation of inelastic deformation of natural rock is also outlined. The hypothesis is fundamental in nature, but proposed in a phenomenological manner. Further examinations of the usefulness and potential limitations of the hypothesis in describing other processes, distinct from flow processes in geosystems, are needed.
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Bejan A (2000) Shape and structure: from engineering to nature. Cambridge University Press, New York
Buckingham E (1907) Studies on the movement of soil moisture. Bulletin 38, USDA Bureau of Soils, Washington DC
Clausse M, Meunier F, Reis AH et al (2012) Climate change: in the framework of the constructal law. Int J Global Warming 4:242–260
Collins IF, Houlsby GT (1997) Application of themomechanical principles to the modeling of geotechnical materials. Proc R Soc London, Ser A, Math Phys Eng Sci 453(1964):1975–2001
Dewar RC (2003) Information theory explanation of the fluctuation theorem, maximum entropy production, and self organized criticality in non-equilibrium stationary states. J Phys A: Math Gen 36:631–641
Dewar RC (2005) Maximum entropy production and the fluctuation theorem. J Phys A: Math Gen 38:371–381
Eigen M (2013) Strange simplicity to complex familiarity. Oxford University Press, Oxford, UK
Fjær E, Holt RM, Horsrud P (2008) Petroleum related rock mechanics, 2nd edn. Elsevier, Boston
Getling AV (1998) Rayleigh Benard convection: structures and dynamics. World Scientific, Singapore
Glansdorff P, Prigogine I (1978) Thermodynamic theory of structure, stability and fluctuations. Wiley-Interscience, New York
Hansen NR, Schreyer HL (1994) A thermodynamically consistent framework for theories of elastoplasticity coupled with damage. Int J Solids Structures 31(3):359–389
Koschmieder KL (1993) Benard cells and Taylor vortices. Cambridge University Press, New York
Krajcinovic D (1989) Damage mechanics. Mech Mater 8:117–197
Li GA (2003) Study on the application of irreversible thermodynamics in the problems of porous medium seepage. Dissertation for Doctoral Degree, Zhejiang University, China
Liu HH (2011a) A note on equations for steady-state optimal landscapes. Geophys Res Letter. doi:10.1029/2011GL047619
Liu HH (2011b) A conductivity relationship for steady-state unsaturated flow processes under optimal flow conditions. Vadose Zone J. doi:10.2136/vzj2010.0118
Liu HH (2014) A thermodynamic hypothesis regarding optimality principles for flow processes in geosystems. Chin Sci Bull 59(16):1880–1884
Malkus WVR, Veronis G (1958) Finite amplitude cellular convection. J Fluid Mech 4:225–260
Martyushev LM, Seleznev VD (2006) Maximum entropy production principle in physics, chemistry and biology. Phys Rep 426:1–45
Nieven RK (2010) Minimization of a free-energy-like potential for non-equilibrium flow systems at steady state. Phil Trans R Soc B2010(365):1213–1331. doi:10.1098/rstb.2009.0296
Ozawa H, Ohmura A, Lorenz R et al (2003) The second law of thermodynamics and the global climate system: a review of the maximum entropy production principle. Rev Geophys. doi:10.1029/2002RG000113
Paltridge GW (1975) Global dynamics and climate—a system of minimum entropy exchange. Quart J R Met Soc 101:475–484
Paltridge GW (1978) The steady-state format of global climate. Quart J R Met Soc 104:927–945
Paltridge GW (2009) A Story and a recommendation about the principle of maximum entropy production. Entropy. doi:10.3390/e11040945
Prigogine I (1955) Introduction to thermodynamics of irreversible processes. Interscience Publishers, New York
Rinaldo A, Rodriguez-Iturbe I, Rigon A et al (1992) Minimum energy and fractal structures of drainage networks. Water Resour Res 28:2183–2191
Rodriguez-Iturbe I, Rinaldo A, Rigon A (1992) Energy dissipation, runoff production and the three-dimensional structure of river basins. Water Resour Res 28(4):1095–1103
Sonnino G, Evslin J (2007) The minimum rate of dissipation principle. Phys Lett A 365:364–369
Ziegler H (1963) Some extremum principles in irreversible thermodynamics with application to continuum mechanics. In: Sneddon IN, Hill R (eds) Progress in solid mechanics, vol 4. Interscience Publishers, New York
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Liu, HH. (2017). A Thermodynamic Hypothesis Regarding Optimality Principles for Flow Processes in Geosystems. In: Fluid Flow in the Subsurface. Theory and Applications of Transport in Porous Media, vol 28. Springer, Cham. https://doi.org/10.1007/978-3-319-43449-0_4
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DOI: https://doi.org/10.1007/978-3-319-43449-0_4
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