Maximum entropy production and constructal law: Variable conductance and branched flow

Year 2022, , 73 - 79, 30.12.2022

Phillip Johnson

https://doi.org/10.14744/seatific.2022.0006

Abstract

Within the scope of modern thermodynamics, several new principles have been advanced. Yet a coherent picture has not yet fully emerged beyond classical thermodynamics, in part because of the disparate nature of these principles. This work analyzes two such principles, that of maximum entropy production and also the constructal law. These ideas are compared in two examples scenarios, atmospheric convection and riverbed generation. It is shown that both ideas utilized a flow network with variable conductivity, particularly that of a branched system. Comparison is made to show underlying shared principles.

Keywords

Thermodynamics, Constructal Theory, Entropy Production, Transport phenomena

References

• Bejan, A. (1996). Street network theory of organization in nature. Journal of Advanced Transportation, 30(2), 85–107.
• Bejan, A. (1997). Constructal-theory network of conducting paths for cooling a heat generating volume. International Journal of Heat and Mass Transfer, 40(4), 799–816.
• Bejan, A. (2010). Design in nature, thermodynamics, and the constructal law: Comment on “Life, hierarchy, and the thermodynamic machinery of planet Earth” by A. Kleidon. Physics of Life Reviews, 7(4), 467–470.
• Bejan, A. (2016). Advanced engineering thermodynamics. John Wiley & Sons.
• Bejan, A. (2018). Thermodynamics today. Energy, 160, 1208–1219.
• Bejan, A. (2020). Discipline in thermodynamics. Energies, 13(10), Article 2487.
• Bejan, A., & Errera, M. R. (1997). Deterministic tree networks for fluid flow: geometry for minimal flow resistance between a volume and one point. Fractals, 5(04), 685–695.
• Bejan, A., & Lorente, S. (2004). The constructal law and the thermodynamics of flow systems with configuration. International Journal of Heat and Mass Transfer, 47(14-16), 3203–3214.
• Bejan, A., & Lorente, S. (2010). The constructal law of design and evolution in nature. Philosophical Transactions of the Royal Society B: Biological Sciences, 365(1545), 1335–1347.
• Bejan, A., & Tsatsaronis, G. (2021). Purpose in thermodynamics. Energies, 14(2), Article 408.
• Bruers, S., Maes, C., & Netočný, K. (2007). On the validity of entropy production principles for linear electrical circuits. Journal of Statistical Physics, 129(4), 725–740.
• De Groot, S. R., & Mazur, P. (1984). Non-equilibrium thermodynamics. Courier Corporation.
• Dewar, R. (2003). Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states. Journal of Physics A: Mathematical and General, 36(3), 631–641.
• Errera, M. R., & Bejan, A. (1998). Deterministic tree networks for river drainage basins. Fractals, 6(03), 245–261.
• Glansdorff, P., & Prigogine, I. (1971). Thermodynamic theory of structure, stability and fluctuations. John Willey & Sons.
• Kleidon, A. (2009). Nonequilibrium thermodynamics and maximum entropy production in the Earth system. Naturwissenschaften, 96(6), 1–25.
• Kleidon, A. (2010). A basic introduction to the thermodynamics of the Earth system far from equilibrium and maximum entropy production. Philosophical Transactions of the Royal Society B: Biological Sciences, 365(1545), 1303–1315.
• Kleidon, A., Malhi, Y., & Cox, P. M. (2010). Maximum entropy production in environmental and ecological systems. Philosophical Transactions of the Royal Society B, 365(1545), 1297–1302.
• Kleidon, A., Zehe, E., Ehret, U., & Scherer, U. (2013). Thermodynamics, maximum power, and the dynamics of preferential river flow structures at the continental scale. Hydrology and Earth System Sciences, 17(1), 225–251.
• Martyushev, L. M., & Seleznev, V. D. (2006). Maximum entropy production principle in physics, chemistry and biology. Physics Reports, 426(1), 1–45.
• Niven, R. K. (2010). Simultaneous extrema in the entropy production for steady-state fluid flow in parallel pipes. Journal of Non-Equilibrium Thermodynamics, 35(3), 1–13.
• Onsager, L. (1931a). Reciprocal relations in irreversible processes. I. Physical Review, 37(4), Article 405.
• Onsager, L. (1931b). Reciprocal Relations in Irreversible Processes. II. Physical Review, 38(12), 2265–2279.
• Paltridge, G. W. (1978). The steady-state format of global climate. Quarterly Journal of the Royal Meteorological Society, 104(442), 927–945.
• Prigogine, I. (1955). Thermodynamics of irreversible processes. Thomas.
• Reis, A. H. (2006). Constructal view of scaling laws of river basins. Geomorphology, 78(3-4), 201–206.
• Reis, A. H. (2014). Use and validity of principles of extremum of entropy production in the study of complex systems. Annals of Physics, 346, 22–27.
• Reis, A. H., & Bejan, A. (2006). Constructal theory of global circulation and climate. International Journal of Heat and Mass Transfer, 49(11-12), 1857–1875.
• Županović, P., Juretić, D., & Botrić, S. (2004). Kirchhoff's loop law and the maximum entropy production principle. Physical Review E, 70(5), Article 056108.