Natural selection for least action

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 464, Issue 2099, 2008, Pages 3055-3070

  Kaila, Ville R I ^a   Annila, Arto ^a,b  

^a UNIVERSITY OF HELSINKI   (Finland)

^b UNIVERSITY OF HELSINKI   (Finland)

Author keywords

Coordinate; Energy transfer; Entropy; Evolution; Metric; Natural process

Indexed keywords

DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); INTEGRAL EQUATIONS; LAWS AND LEGISLATION;

COORDINATE; ENERGY DENSITIES; ENERGY TRANSFER; ENTROPY; EQUATION OF MOTION; EVOLUTION; INTEGRAL FORM; METRIC; NATURAL PROCESS; NATURAL SELECTION; PRINCIPLE OF LEAST ACTION; SECOND LAW OF THERMODYNAMICS; SECOND-LAW; SHORTEST PATHS;

EQUATIONS OF MOTION;

EID: 52949104099     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2008.0178     Document Type: Article

References (64)

1. Aharonov, Y. & Bohm, D. 1959 Significance of electromagnetic potentials in quantum theory. Phys. Rev. 115, 485-491. (doi:10.1103/PhysRev.115.485)
2. Atkins, P. W. & de Paula, J. 2006 Physical chemistry, 8th edn. New York, NY: Oxford University Press.
3. Bayes, T. 1763 A Letter from the Late Reverend Mr. Thomas Bayes, F. R. S. to John Canton, M. A. and F. R. S. Phil. Trans. 53, 269-271. (doi:10.1098/rstl.1763.0044)
4. Berry, M. 2001 Principles of cosmology and gravitation. Cambridge, UK: Cambridge University Press.
5. Boltzmann, L. 1905 Populäre Schriften. Leipzig, Germany: Barth. [Partially transl. Theoretical physics and philosophical problems by B. McGuinness, Reidel, Dordrecht, 1974.]
6. Boltzmann, L. 1974 The second law of thermodynamics. In Ludwig Boltzmann, theoretical physics and philosophical problems, selected writings (ed. B. McGinness). Dordrecht, NY: Reidel.
7. Brillouin, L. 1963 Science and information theory. New York, NY: Academic Press.
8. Brooks, D. R. & Wiley, E. O. 1988 Evolution as entropy: toward a unified theory of biology, 2nd edn. Chicago, IL: University of Chicago Press.
9. Carroll, S. 2004 Spacetime and geometry: an introduction to general relativity. London, UK: Addison Wesley.
10. Chaisson, E. J. 1998 The cosmic environment for the growth of complexity. Biosystems 46, 13-19. (doi:10.1016/S0303-2647(97)00076-2)
11. Chow, B. & Knopf, D. 2004 The Ricci flow: an introduction. Mathematical Surveys and Monographs, 110. Providence, RI: American Mathematical Society.
12. Darwin, C. 1859 On the origin of species. London, UK: John Murray.
13. de Maupertuis, P. L. M. 1744 Accord de différentes lois de la nature qui avaient jusqu'ici paru incompatibles. Mém. As. Sc. Paris 417.
14. de Maupertuis, P. L. M. 1746 Les loix du mouvement et du repos déduites d'un principe métaphysique. Mém. Ac. Berlin 267.
15. Eddington, A. S. 1928 The nature of physical world. New York, NY: MacMillan.
16. Euler, L. 1744 Methodus inveniendi Lineas curvas maximi minive proprietate gaudentes. Lausanne: Bousquet. [Reprinted in Leonhardi Euleri Opera Omnia. Series 1, vol. 24. Zurich: Orell Fuessli, 1952.]
17. Feynman, R. P. 1948 Space-time approach to non-relativistic quantum mechanics. Rev. Mod. Phys. 20, 367-387. (doi:10.1103/RevModPhys. 20.367)
18. Feynman, R. P. & Hibbs, A. R. 1965 Quantum mechanics and path integrals. New York, NY: McGraw-Hill.
19. Foster, J. & Nightingale, J. D. 1994 A short course in general relativity. New York, NY: Springer.
20. Gibbs, J. W. 1993-1994 The scientific papers of J. Willard Gibbs. Woodbridge, CT: Ox Bow Press.
21. Gleyzes, S., Kuhr, S., Guerlin, C., Bernu, J., Deléglise, S., Busk Hoff, U., Brune, M., Raimond, J. M. & Haroche, S. 2007 Quantum jumps of light recording the birth and death of a photon in a cavity. Nature 446, 297-300. (doi:10.1038/nature05589)
22. Grönholm, T. & Annila, A. 2007 Natural distribution. Math. Biosci. 210, 659-667. (doi:10.1016/j.mbs.2007.07.004)
23. Gyarmati, I. 1970 Nonequilibrium thermodynamics: field theory and variational principles. New York, NY: Springer.
24. Hamilton, W. R. 1834 On a general method in dynamics; by which the study of the motions of all free systems of attracting or repelling points is reduced to the search and differentiation of one central relation or characteristic function. Phil. Trans. R. Soc. Lond. 124, 247-308. (doi:10.1098/rstl.1834.0017)
25. Hamilton, W. R. 1835 Second essay on a general method in dynamics. Phil. Trans. R. Soc. Lond. 125, 95-144. (doi:10.1098/rstl.1835. 0009)
26. Hanc, J. & Taylor, E. F. 2004 From conservation of energy to the principle of least action: a story line. Am. J. Phys. 72, 514-521. (doi:10.1119/1.1645282)
27. Hanc, J., Taylor, E. F. & Tuleja, S. 2004 Deriving Lagrange's equations using elementary calculus. Am. J. Phys. 72, 510-513. (doi:10.1119/1.1603270)
28. Jaakkola, S., Sharma, V. & Annila, A. 2008a Causeof chirality consensus. Curr. Chem. Biol. 2, 53-58.
29. Jaakkola, S., El-Showk, S. & Annila, A. 2008b The driving force behind genomic diversity. Biophys. Chem. 134, 232-238. (doi:10.1016/j.bpc.2008.02.006) (See also http://arxiv.org/abs/0807.0892)
30. Jaynes, E. T. 2003 Probability theory: the logic of science (ed. G. L. Bretthorst). Cambridge, UK: Cambridge University Press.
31. Karnani, M. & Annila, A. In press. Gaia again. Biosystems. (doi:10.1016/j.biosystems.2008.07.003)
32. Kondepudi, D. & Prigogine, I. 1998 Modern thermodynamics. New York, NY: Wiley.
33. Kullback, S. 1959 Information theory and statistics. New York, NY: Wiley.
34. Lagrange, J. L. 1788 Mechanique analytic. Paris. [Transl. by V. N. Vagliente & A. Boissonnade, Kluwer Academic, Dordrecht, The Netherlands, 2001.]
35. Landau, L. D. & Lifshitz, E. M. 1975 The classical theory of fields. London, UK: Pergamon.
36. Landauer, R. 1961 Irreversibility and heat generation in the computing process. IBM J. Res. Dev. 5, 183-191.
37. Lee, J. M. 2003 Introduction to smooth manifolds. New York, NY: Springer.
38. Lorenz, R. D. 2002 Planets, life and the production of entropy. Int. J. Astrobiol. 1, 3-13. (doi:10.1017/S1473550402001027)
39. Lotka, A. J. 1922 Natural selection as a physical principle. Proc. Natl Acad. Sci. USA 8, 151-154. (doi:10.1073/pnas.8.6.151)
40. Lotka, A. J. 1925 Elements of physical biology. Baltimore, MD: Williams and Wilkins.
41. Lovelock, J. E. 1988 The ages of Gaia. Oxford, UK: Oxford University Press.
42. Maslov, V. N. 1991 Thermodynamic basis of the principle of least action. Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, (Russ. Phys. J.) 5, 53-59.
43. Moiseev, N. N. 1987 Development algorithms in Russian. Moscow, Russia: Nauka.
44. Nesbet, R. K. 2003 Variational principles and methods in theoretical physics and chemistry. Cambridge, UK: Cambridge University Press.
45. Newton, I. 1687 The principia. [Transl. by A. Motte & D. Adee, New York, 1846.]
46. Noether, E. 1918 Invariante variationprobleme. Nach. v.d. Ges. d. Wiss zu Goettingen, Mathphys. Klasse 235-257.
47. [English transl. by Tavel, M. A. Invariant variation problem. Transp. Theory Stat. Phys. 1, 183-207, 1971.]
48. Poynting, J. H. 1920 Collected scientific papers. London, UK: Cambridge University Press.
49. Ritz, W. & Einstein, A. 1909 Zum gegenwärtigen stand des strahlungsproblems. Phys. Z. 10, 323-324.
50. Salthe, S. N. 1993 Development and evolution: complexity and change in biology. Cambridge, MA: MIT Press.
51. Schieve, W. C., Horwitz, L. P. & Levitan, J. 1989 Numerical study of Zeno and anti-Zeno effects in a local potential model. Phys. Lett. A 136, 264-268. (doi:10.1016/0375-9601(89)90811-6)
52. Schneider, E. D. & Kay, J. J. 1994 Life as a manifestation of the second law of thermodynamics. Math. Comput. Model. 19, 25-48. (doi:10.1016/0895-7177(94)90188-0)
53. Schrödinger, E. 1948 What is life? The physical aspects of the living cell. Cambridge, UK: Cambridge University Press.
54. Schwarzschild, K. 1916 Über das Gravitationsfeld eines Massenpunktes nach der Einstein'schen Theorie. Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften 1, 189-196.
55. Shannon, C. E. 1948 A mathematical theory of communication. Bell Syst. Tech. J. 27, 379-423. (See also pp. 623-656.)
56. Sharma, V. & Annila, A. 2007 Natural process natural selection. Biophys. Chem. 127, 123-128. (doi:10.1016/j.bpc.2007.01.005)
57. Stöltzner, M. 2003 The principle of least action as the logical empiricist's shibboleth. Stud. Hist. Philos. Mod. Phys. 34, 285-318. (doi:10.1016/S1355-2198(03)00002-9)
58. Strogatz, S. H. 2000 Nonlinear dynamics and chaos with applications to physics, biology, chemistry and engineering. Cambridge, MA: Westview.
59. Sudarshan, E. C. G. & Misra, B. 1977 The Zeno's paradox in quantum theory. J. Math. Phys. 18, 756-763. (doi:10.1063/1.523348)
60. Taylor, E. F. & Wheeler, J. A. 2000 Exploring black holes: an introduction to general relativity. New York, NY: Addison-Wesley Longman.
61. Ulanowicz, R. E. & Hannon, B. M. 1987 Life and the production of entropy. Proc. R. Soc. B 232, 181-192. (doi:10.1098/rspb.1987. 0067)
62. Weinberg, S. 1972 Gravitation and cosmology, principles and applications of the general theory of relativity. New York, NY: Wiley.
63. Weyl, H. 1949 Philosophy of mathematics and natural science. Princeton, NJ: Princeton University Press.
64. Zeh, H. D. 2007 The physical basis of the direction of time, 5th edn. Berlin, Germany: Springer.