On intractable tracks

Physics Essays

Volumn 25, Issue 2, 2012, Pages 233-238

  Annila, Arto ^a   Salthe, Stanley ^b  

^a UNIVERSITY OF HELSINKI   (Finland)

^b BINGHAMTON UNIVERSITY   (United States)

Author keywords

Energy dispersal; Evolution; Free energy; Hierarchy; Principle of least action; Quantization

Indexed keywords

EID: 84863930658     PISSN: 08361398     EISSN: None     Source Type: Journal    
DOI: 10.4006/0836-1398-25.2.233     Document Type: Article

References (50)

1. P.-L. M. Maupertuis, Mém. As. Sc. Paris 417 (1744).
2. J.-L. Lagrange, Mechanique analytique (Chez la Veuve Desaint, Paris, 1788);
3. republished as A. C. Boissonnade and V. N. Vagliente (trans.), Analytical Mechanics (Kluwer Academic, Dordrecht, 2001).
4. W. R. Hamilton, Phil. Trans. R. Soc. Part I, 247-308, Part II, 95-144 (1834-1835).
5. D. Beeson, Maupertuis: An Intellectual Biography (Voltaire Foundation, Oxford, 1992).
6. P.-L. M. Maupertuis, Histoire de l'Academie Royale des Science et des Belles Lettres, pp. 267-294 (1746).
7. L. Euler, Methodus inveniendi lineas curvas maximi minive proprietate gaudentes (Marcum-Michaelem Bousquet & Socios, Lausanne and Geneva, 1744).
8. J. S. Koenig, Nova Acta Eruditorum, pp. 125-135, 162-176 (1751).
9. E. Ramm, GAMM-Mitt. 34, 164 (2001).
10. E. Du Châtelet, Institutions de Physique (Prault, Paris, 1740).
11. J. H. Poynting, Collected Scientific Papers (Cambridge University Press, London, 1920).
12. I. Prigogine and J. M. Wiame, Experientia 2, 451 (1946).
13. G. Kampis, Self-modifying Systems in Biology and Cognitive Science: A New Framework for Dynamics, Information and Evolution (Pergamon Press, London 1991).
14. J. H. Silverman, The Arithmetic of Elliptic Curves (Springer-Verlag, New York, 1992).
15. P. Tuisku, T. K. Pernu, and A. Annila, Proc. R. Soc. A. 465, 1173 (2009).
16. V. Sharma and A. Annila, Biophys. Chem. 127, 123 (2007).
17. V. R. I. Kaila and A. Annila, Proc. R. Soc. A 464, 3055 (2008).
18. A. Annila, Entropy 12, 2333 (2010).
19. J. H. Poincaré , Acta Mathematica 13, 1 (1890).
20. M. Sipser, Introduction to the Theory of Computation (Pws Publishing, New York, 2001).
21. A. S. Fraenkel, Bull. Math. Biol. 55, 1199 (1993).
22. V. Sharma, V. R. I. Kaila, and A. Annila, Physica A 388, 851 (2009).
23. A. Annila, ISRN Comp. Math. (2012), pp. 1-15; See http://www.isrn.com/ journals/cm/aip/321372/, http://arxiv.org/abs/0906.1084.
24. R. P. Feynman, Rev. Mod. Phys. 20, 367 (1948).
25. P. Szekeres, A Course in Modern Mathematical Physics (Cambridge University Press, Cambridge, U.K., 2004).
26. C. Darwin, On the Origin of Species (John Murray, London, 1859).
27. L. Boltzmann, Populäre Schriften (Barth, Leipzig, 1905).
28. J. W. Gibbs, The Scientific Papers of J. Willard Gibbs (Ox Bow Press, Woodbridge, U.K., 1993-1994).
29. S. P. Mahulikar and H. Harwig, Physica Scripta 70, 212 (2004).
30. R. C. Dewar, J. Phys. A: Math. Gen. 36, 631 (2003).
31. E. Noether, Nach. v.d. Ges. d. Wiss zu Goettingen, Mathphys. Klasse 235 (1918)
32. M. A. Tavel (trans.), Transp. Theory Stat. Phys. 1, 183 (1971).
33. R. D. Mattuck, A Guide to Feynman Diagrams in the Many-Body Problem (McGraw-Hill, New York, 1976).
34. M. Alonso and E. J. Finn, Fundamental University Physics Vol. III: Quantum and Statistical Physics (Addison-Wesley, Reading, MA, 1983).
35. K. H. Rosen, Elementary Number Theory and Its Applications (Addison-Wesley, Reading, 1993).
36. G. Georgiev and I. Georgiev, Open Syst. Inf. Dyn. 9, 371 (2002).
37. S. N. Salthe, Entropy 6, 327 (2004).
38. H. B. G. Casimir and D. Polder, Phys. Rev. 73, 360 (1948).
39. Y. Aharonov and D. Bohm, Phys. Rev. 115, 485 (1959).
40. C. M. Wilson, G. Johansson, A. Pourkabirian, M. Simoen, J. R. Johansson, T. Duty, F. Nori, and P. Delsing, Nature 479, 376 (2011).
41. C. L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut, M. Limon, S. S. Meyer, L. Page, D. N. Spergel, G. S. Tucker, E. Wollack, E. L. Wright, C. Barnes, M. R. Greason, R. S. Hill, E. Komatsu, M. R. Nolta, N. Odegard, H. V. Peiris, L. Verde, and J. L. Weiland, Astrophys. J. Supp. 148, 1 (2003).
42. A. Unsöld and B. Baschek, The New Cosmos: An Introduction to Astronomy and Astrophysics (Springer-Verlag, New York, 2002).
43. N. Eldredge and S. J. Gould, Punctuated Equilibria: An Alternative to Phyletic Gradualism, in T. J. M. Schopf (ed.), Models in Paleobiology (Freeman Cooper, San Francisco, 1972), p. 82.
44. T. Mäkelä and A. Annila, Phys. Life Revs. 7, 477 (2010).
45. A. Annila and S. Salthe, Entropy 11, 606 (2009).
46. A. Annila and S. Salthe, J. Non-Equilb. Thermodyn. 35, 301 (2010).
47. P. Bak, How Nature Works: The Science of Self-Organized Criticality (Copernicus, New York, 1996).
48. C. H. Waddington, The Epigenetics of Birds (Cambridge University Press, Cambridge, U.K., 1953).
49. L. Van Valen, Evol. Theor. 1, 1 (1973).
50. S. H. Strogatz, Nonlinear Dynamics and Chaos with Applications to Physics, Biology, Chemistry and Engineering (Westview, Cambridge, U.K., 2000).