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A unified view of transport equations

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  • Secrest, J.A.
  • Conroy, J.M.
  • Miller, H.G.

Abstract

Distribution functions of many static transport equations are found using the Maximum Entropy Principle. The equations of constraint which contain the relevant dynamical information are simply the low-lying moments of the distributions. Systems subject to conservative forces have also been considered. In this approach, determining the solutions to the transport equations no longer requires solving a partial differential equation but instead experimentally determining the low-lying moments and potentials.

Suggested Citation

  • Secrest, J.A. & Conroy, J.M. & Miller, H.G., 2020. "A unified view of transport equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    • Handle: RePEc:eee:phsmap:v:547:y:2020:i:c:s0378437120301552
    DOI: 10.1016/j.physa.2020.124403
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    1. Bouchet, Freddy & Gupta, Shamik & Mukamel, David, 2010. "Thermodynamics and dynamics of systems with long-range interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(20), pages 4389-4405.
    2. Lee, Kwonmoo & Sung, Wokyung, 2002. "Ion transport and channel transition in biomembranes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 315(1), pages 79-97.
    3. Malaza, E.D. & Miller, H.G. & Plastino, A.R. & Solms, F., 1999. "Approximate time dependent solutions of partial differential equations: the MaxEnt-Minimum Norm approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 265(1), pages 224-234.
    4. Alves, Alexandre & Dias, Alex G. & da Silva, Roberto, 2015. "Maximum Entropy Principle and the Higgs boson mass," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 420(C), pages 1-7.
    5. Bartiromo, Rosario, 2013. "Maximum entropy distribution of stock price fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(7), pages 1638-1647.
    6. El-Wakil, S.A. & Elhanbaly, A. & Abdou, M.A., 2003. "Maximum entropy method for solving the collisional Vlasov equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 213-228.
    7. Rosario Bartiromo, 2011. "Maximum entropy distribution of stock price fluctuations," Papers 1106.4957, arXiv.org, revised Oct 2013.
    8. Theodoros Christoudias & Yiannis Proestos & Jos Lelieveld, 2014. "Atmospheric Dispersion of Radioactivity from Nuclear Power Plant Accidents: Global Assessment and Case Study for the Eastern Mediterranean and Middle East," Energies, MDPI, vol. 7(12), pages 1-17, December.
    9. Ghoshal, Koeli & Kumbhakar, Manotosh & Singh, Vijay P., 2019. "Distribution of sediment concentration in debris flow using Rényi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 267-281.
    10. Hazan, Aurélien, 2019. "A maximum entropy network reconstruction of macroeconomic models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 519(C), pages 1-17.
    11. Diambra, L., 2008. "Clustering gene expression by dynamics: A maximum entropy approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2187-2196.
    12. Caldas, Denise & Chahine, Jorge & Filho, Elso Drigo, 2014. "The Fokker–Planck equation for a bistable potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 92-100.
    13. Dobovišek, Andrej & Markovič, Rene & Brumen, Milan & Fajmut, Aleš, 2018. "The maximum entropy production and maximum Shannon information entropy in enzyme kinetics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 220-232.
    14. Schönfeldt, J-H. & Jimenez, N. & Plastino, A.R. & Plastino, A. & Casas, M., 2007. "Maximum entropy principle and classical evolution equations with source terms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 573-584.
    15. Schönfeldt, J.-H. & Plastino, A.R., 2006. "Maximum entropy approach to the collisional Vlasov equation: Exact solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 408-416.
    16. Giffin, Adom, 2009. "From physics to economics: An econometric example using maximum relative entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1610-1620.
    17. Zhang, Xuguang & Shu, Xiaohu & He, Zhen, 2019. "Crowd panic state detection using entropy of the distribution of enthalpy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 935-945.
    18. Adom Giffin, 2009. "From Physics to Economics: An Econometric Example Using Maximum Relative Entropy," Papers 0901.0401, arXiv.org.
    19. Batle, J & Casas, M & Plastino, A.R & Plastino, A, 2002. "Supersymmetry and the q-MaxEnt treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(1), pages 316-322.
    20. Zhang, Yongping & Shang, Pengjian & Xiong, Hui, 2019. "Multivariate generalized information entropy of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1212-1223.
    21. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    22. Plastino, A.R. & Casas, M. & Plastino, A., 2000. "A nonextensive maximum entropy approach to a family of nonlinear reaction–diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 280(3), pages 289-303.
    23. El-Wakil, S.A. & Abulwafa, E.M. & Abdou, M.A. & Elhanbaly, A., 2002. "Maximum-entropy approach with higher moments for solving Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 315(3), pages 480-492.
    24. Plastino, A.R. & Plastino, A., 1995. "Non-extensive statistical mechanics and generalized Fokker-Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 222(1), pages 347-354.
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