Skip to main content
SpringerLink
Log in

On the affordances of the MaxEP principle

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

Optimality principles have long been popular in the natural sciences and enjoyed much successes in various applications. However these principles seem to be disparate, each applied in limited contexts and there are far too many of them causing some consternation among scientists and philosophers of science regarding the ad-hoc nature of the optimality arguments. In this paper, we discuss the Maximum entropy production (MaxEP) as a plausible over-arching principle to understand stable configurations in fluid mechanics and related problems. The MaxEP being based upon sound physical arguments and in the immutable laws of thermodynamics along with the fact that it has been successfully co-opted across disciplines makes it worthy of attention. We discuss various physical and metaphysical aspects of this principle and use it to analyze some model problems regarding patterns in particle sedimentation such as sedimentation of a particle in Newtonian and non-Newtonian fluids and stable deformation of a falling droplet.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R.K. Niven, J. Non-Equilibrium Thermodynamics 35, 3 (2010).

    Article  Google Scholar 

  2. H. Ziegler, An Introduction to Thermodynamics (North-Holland, Amsterdam, 1983).

  3. L.M. Martyushev, V.D. Seleznev, Chem. Biol. Phys. Rep. 426, 1 (2006).

    ADS  MathSciNet  Google Scholar 

  4. L. Onsager, Phys. Rev. 37, 405 (1931).

    Article  ADS  Google Scholar 

  5. L. Onsager, Phys. Rev. 38, 2265 (1931).

    Article  ADS  MATH  Google Scholar 

  6. I. Prigogine, Introduction to Thermodynamics of Irreversible Processes (Interscience Publishers, New York, 1955).

  7. S. Bordel, Physica A 389, 21 (2010).

    Article  MathSciNet  Google Scholar 

  8. A. Vaidya, in MaxEP and stable configurations in fluid solid interactions, Beyond the Second Law: Entropy Production and Non-Equilibrium Systems (Book Series: Understanding Complex Systems), edited by R.C. Dewar, C. Lineweaver, R. Niven, K. Regenauer-Lieb (Springer Verlag, 2013).

  9. A. Bejan, Shape and Structure, from Engineering to Nature (Cambridge University Press, Cambridge, 2000).

  10. A. Bejan, S. Lorente, Philos. Trans. Roy. Soc. B 365, 1545 (2010).

    Article  Google Scholar 

  11. A. Bejan, S. Lorente, J. Appl. Phys. 113, 151301 (2013).

    Article  ADS  Google Scholar 

  12. A. Bejan, S. Lorente, J. Appl. Phys. 100, 041301 (2006).

    Article  ADS  Google Scholar 

  13. K.R. Rajagopal, A.R. Srinivasa, Int. J. Plast. 14, 10 (1998).

    Google Scholar 

  14. K.R. Rajagopal, A.R. Srinivasa, ZAMP 50, 459 (1999).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  15. K.R. Rajagopal, A.R. Srinivasa, J. Non-Newtonian Fluid Mech. 88, 207 (2000).

    Article  MATH  Google Scholar 

  16. E.D. Schneider, J.J. Kay, Math. Comput. Mod. 19, 6 (1994).

    Article  Google Scholar 

  17. G.P. Beretta, Phys. Rev. E 73, 026113 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  18. G.P. Beretta, J. Math. Phys. 25, 1507 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  19. R. Swenson, Int. J. General Systems 21, 2 (1992).

    Google Scholar 

  20. R. Dewar, J. Phys. A 36, 3 (2003).

    Article  MathSciNet  Google Scholar 

  21. R. Dewar, Entropy 11, 4 (2009).

    Article  MathSciNet  Google Scholar 

  22. A. Kleidon, Philos. Trans. Roy. Soc. A 370, 1012 (2012).

    Article  ADS  Google Scholar 

  23. A. Kleidon, R.D. Lorenz, Non-Equilibrium Thermodynamics and the Production of Entropy: Life, Earth, and Beyond (Springer, Berlin, 2005).

  24. R.K. Niven, Phys. Rev. E 80, 2 (2009).

    Article  Google Scholar 

  25. H. Ozawa, A. Ohmaru, R.D. Lorenz, T. Pujol, Rev. Geophys. 41, 4 (2003).

    Article  Google Scholar 

  26. B.J. Chung, A. Vaidya, Physica D 237, 22 (2008).

    Article  MathSciNet  Google Scholar 

  27. B.J. Chung, Vaidya, Appl. Math. Comput. 218, 7 (2011).

    Google Scholar 

  28. J. Gibson, The Ecological Approach to Visual Perception, New Ed edition (Psychology Press, 1986).

  29. Routledge Encyclopedia of Philosophy, Version 1.0, (Routledge, London and New York, 1998).

  30. P.J.H. Schoemaker, Behav. Brain Sci. 14, 2 (1991).

    Google Scholar 

  31. R.P. Feynman, The Feynman Lectures on Physics, 2nd edn. (Addison Wesley, 2005), Vol. 1.

  32. E. Nagel, The Structure of Science (Harcourt, Brace & World, New York, 1961).

  33. R. Macklin, British J. Philos. Sci. 19, 345 (1969).

    Article  Google Scholar 

  34. B. Russell, On the notion of cause, in Mysticism and Logic and other essay (Bibliolife, 2009).

  35. E.T. Jaynes, Ann. Rev. Phys. Chem. 31, 579 (1980).

    Article  ADS  Google Scholar 

  36. G.W. Paltridge, Quart. J. Roy. Meteor. Soc. 104, 927 (1975).

    Article  ADS  Google Scholar 

  37. S. Bruers, J. Phys. A 40, 27 (2007).

    Article  MathSciNet  Google Scholar 

  38. S. Ede, Art and Science (I.B. Tauris, 2005).

  39. P. Hoffman, The Man Who Loved Only Numbers, 1st edn. (Hyperion, New York, 1998).

  40. S. Chandrasekhar, Bulletin Am. Acad. Arts Sci. 43, 3 (1989).

    Google Scholar 

  41. L.S. Feuer, Philos. Sci. 24, 2 (1957).

    Article  Google Scholar 

  42. A. Rosenblueth, N. Wiener, J. Bigelow, Philos. Sci. 10, 1 (1943).

    Google Scholar 

  43. B.E. Hobbs, A. Ord, K. Regenbauer-Lieb, J. Struct. Geol. 33, 220 (2011).

    Article  Google Scholar 

  44. H.J. Kreuzer, Nonequilibrium Thermodynamics and its Statistical Foundations (Clarendon Press, Oxford, 1981).

  45. E. Lorenz, Generation of available potential energy and the intensity of the general circulation. Scientific Report No. 1, UCLA, Dept. of Meteorology, 1955.

  46. B. Russell, ABC of Relativity (Routledge, New York, 1958).

  47. A. Kleidon, Naturwissenschaften 96, 6 (2009).

    Article  Google Scholar 

  48. G. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, 1967).

  49. R. Ghesselini, J. Non-Newtonian Fluid Mech. 46, 2 (1993).

    Google Scholar 

  50. G. Kirchoff, J. Reine Ang. Math. Soc. 71, 237 (1869).

    Google Scholar 

  51. K. Chiba, K. Song, A. Horikawa, Rheol. Acta 25, 280 (1986).

    Article  Google Scholar 

  52. K. Cho, Y.I. Cho, N.A. Park, J. Non-Newtonian Fluid Mech. 45, 1 (1992).

    MathSciNet  Google Scholar 

  53. G.P. Galdi, A. Vaidya, J. Math. Fluid Mech. 3, 2 (2001).

    Article  MathSciNet  Google Scholar 

  54. G.P. Galdi, On the Motion of a Rigid Body in a Viscous Fluid: A Mathematical Analysis with Applications, Handbook of Mathematical Fluid Mechanics (Elsevier Science, Amsterdam, 2002).

  55. H.H. Howard, D.D. Joseph, A.F. Fortes, Int. Video J. Eng. Res. 2, 17 (1992).

    Google Scholar 

  56. D.D. Joseph, Y.J. Liu, J. Rheol. 37, 6 (1993).

    Article  MathSciNet  Google Scholar 

  57. A. Vaidya, Appl. Math. Lett. 18, 12 (2005).

    Article  MathSciNet  Google Scholar 

  58. A. Vaidya, Jpn J. Indus. Appl. Math. 21, 3 (2004).

    Article  MathSciNet  Google Scholar 

  59. D.D. Joseph, J. Feng, J. Non-Newtonian Fluid Mech. 64, 2 (1996).

    Article  Google Scholar 

  60. G.P. Galdi, M. Pokorny, A. Vaidya, D.D. Joseph, J. Feng, Math. Mod. Methods Appl. Sci. 12, 11 (2002).

    Article  MathSciNet  Google Scholar 

  61. L. Chen, S.V. Garimella, J.A. Reizes, E. Leonardi, J. Fluid Mech. 387, 61 (1999).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  62. D. Bhaga, M.E. Weber, J. Fluid Mech. 105, 61 (1981).

    Article  ADS  Google Scholar 

  63. C. I. Christov, P.K. Volkov, J. Fluid Mech. 158, 341 (1985).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  64. R.A. Hartunian, W.R. Sears, J. Fluid Mech. 3, 27 (1957).

    Article  ADS  MATH  Google Scholar 

  65. D.W. Moore, J. Fluid Mech. 6, 113 (1959).

    Article  ADS  MATH  Google Scholar 

  66. G. Ryskin, L.G. Leal, J. Fluid Mech. 148, 1 (1984).

    Article  ADS  MATH  Google Scholar 

  67. T.D. Taylor, A. Acrivos, J. Fluid Mech. 18, 466 (1964).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  68. J.K. Walters, J.F. Davidson, J. Fluid Mech. 12, 408 (1962).

    Article  ADS  Google Scholar 

  69. P.P. Wegener, J.Y. Parlange, Ann. Rev. Fluid Mech. 5, 79 (1973).

    Article  ADS  Google Scholar 

  70. S.F. Hoerner, Fluid-Dynamic Drag. Hoerner Fluid Dynamics (Brick Town, N.J., USA, 1965).

  71. D.F. Young, B.R. Munson, T.H. Okiishi, W.W. Huebsch, A Brief Introduction To Fluid Mechanics, 5th edn. (Wiley, 2010).

  72. C. Horne, C.A. Smith, K. Karamcheti, NASA Technical Paper 3118 (1991).

  73. L. Bertalanffy, General Systems Theory (George Braziller, Inc., New York, 1968).

Download references

Author information

Authors and Affiliations

  1. School of Physics, Astronomy, and Computational Sciences, Center for Computational Fluid Dynamics, George Mason University, Fairfax, VA, 22030, USA

    Bong Jae Chung

  2. Department of Philosophy and Religion, Montclair State University, Montclair, NJ, 07045, USA

    Kirk McDermid

  3. Department of Mathematical Sciences, Montclair State University, Montclair, NJ, 07045, USA

    Ashwin Vaidya

Authors
  1. Bong Jae Chung
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kirk McDermid
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ashwin Vaidya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ashwin Vaidya.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chung, B., McDermid, K. & Vaidya, A. On the affordances of the MaxEP principle. Eur. Phys. J. B 87, 20 (2014). https://doi.org/10.1140/epjb/e2013-40490-7

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2013-40490-7

Keywords

Search

Navigation