Multiscale complexity/entropy

Advances in Complex Systems

Volumn 7, Issue 1, 2004, Pages 47-63

  Bar Yam, Y ^a  

^a NEW ENGLAND COMPLEX SYSTEMS INSTITUTE   (United States)

Author keywords

Complexity; Entropy; Information; Negative information; Scale; Variety

Indexed keywords

COMPUTATIONAL METHODS; CORRELATION METHODS; ENTROPY; INFORMATION ANALYSIS; MICROSCOPIC EXAMINATION; PHASE EQUILIBRIA; QUANTUM THEORY; THERMODYNAMICS;

NEGATIVE INFORMATION; NON-EQUILIBRIUM SYSTEMS; SCALE; VARIETY;

LARGE SCALE SYSTEMS;

EID: 11244272997     PISSN: 02195259     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219525904000068     Document Type: Review

References (56)

1. Maxwell, J. C., Theory of Heat (Appleton, London, 1871).
2. Szilard, L., ber die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen, Z. Physik 53, 840-856 (1929).
3. Brillouin, L., Science and Information Theory (Academic Press, New York, 1956).
4. Landauer, R., Irreversibility and heat generation in the computing process, IBM J. Res. Dev. 3, 183-191 (1961).
5. Bennett, C. H., Logical reversibility of computation, IBM J. Res. Dev. 17, 525-532 (1973).
6. Bennett, C. H., Thermodynamics of computation - A review, Int. J. Theor. Phys. 21, 905-940 (1982).
7. Fredkin, E. and Toffoli, T., Conservative logic, Int. J. of Theor. Phys. 21, 219-253 (1982).
8. Zurek, W. H., Thermodynamic cost of computation, algorithmic complexity and the information metric, Nature 341, 119-124 (1989).
9. Landauer, R., Information is physical, Phys. Today 44, 23-29 (1991).
10. Bar-Yam, Y., Dynamics of Complex Systems (Perseus, 1997), Chaps. 8 and 9.
11. Lindgren, K., Microscopic and macroscopic entropy, Phys. Rev. E38, 4794 (1988).
12. Schrödinger, E., What is Life? (Cambridge University Press, Cambridge, 1944).
13. Shannon, C. E., A mathematical theory of communication, Bell Systems Technical Journal, July and October 1948; reprinted in C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois Press, Urbana, 1963).
14. Shannon, C. E., A mathematical theory of communication, Bell Systems Technical Journal, July and October 1948; reprinted in C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois Press, Urbana, 1963).
15. Jaynes, E. T., Information theory and statistical mechanics, Phys. Rev. 106, 620 (1957).
16. Kolmogorov, A. N., Dokl. Akad. Nauk SSSR 119, 861 (1958); ibid. 124, 754 (1959), Sinai, Ya. G., Dokl. Akad. Nauk SSSR 124, 768 (1959).
17. Kolmogorov, A. N., Dokl. Akad. Nauk SSSR 119, 861 (1958); ibid. 124, 754 (1959), Sinai, Ya. G., Dokl. Akad. Nauk SSSR 124, 768 (1959).
18. Kolmogorov, A. N., Dokl. Akad. Nauk SSSR 119, 861 (1958); ibid. 124, 754 (1959), Sinai, Ya. G., Dokl. Akad. Nauk SSSR 124, 768 (1959).
19. Solomonoff, R. J., Information and Control 7, 1 (1964); ibid. 224 (1964).
20. Solomonoff, R. J., Information and Control 7, 1 (1964); ibid. 224 (1964).
21. Shiryayev, A. N. ed., Selected Works of A. N. Kolmogorov, Volume III: Information Theory and the Theory of Algorithms (Mathematics and Its Applications), (Kluwer, Dordrecht, 1987).
22. Chaitin, G. J., Information, Randomness & Incompleteness, 2nd Edn (World Scientific, Singapore, 1990); Algorithmic Information Theory (Cambridge University Press, Cambridge, 1987).
23. Chaitin, G. J., Information, Randomness & Incompleteness, 2nd Edn (World Scientific, Singapore, 1990); Algorithmic Information Theory (Cambridge University Press, Cambridge, 1987).
24. Carnap, R., Two Essays on Entropy (University of California Press, Berkeley, 1977).
25. Bennett, C. H., Int. J. of Theoretical Physics 21, 905 (1982).
26. Denbigh, K. G. and Denbigh, J. S., Entropy in Relation to Incomplete Knowledge (Cambridge University Press, Cambridge, 1985).
27. Lloyd, S. and Pagels, H., Complexity as Thermodynamic Depth, Annals of Physics 188, 186-213 (1988).
28. Zurek, W. H. ed., Complexity, Entropy and the Physics of Information (Addison-Wesley, 1990).
29. Tononi, G., Sporns, O. and Edelman, G. M., Proc. Nat. Acad. Sci. 91, 5033 (1994).
30. Gell-Mann, M., Complexity 1, 16-19 (1995).
31. Toffoli, T., Biafore, M. and Leo, J., eds., Proc. 4th Workshop on Physics and Computation (PhysComp96) New England Complex Systems Institute (1996).
32. Gell-Mann, M. and Lloyd, S., Complexity 2, 44-52 (1996).
33. Lindgren, K., Moore, C. and Nordahl, M., Complexity of two-dimensional patterns, J. of Stat. Phys. 91, 909-951 (1998).
34. Wolpert, D. H. and Macready, W. G., Self-dissimilarity: An empirically observable complexity measure, in Unifying Themes in Complex Systems, ed. Y. Bar-Yam, (Perseus Press, 2000), pp. 626-643.
35. Andrienko, Yu. A., Brilliantov, N. V. and Kurths, J., Complexity of two-dimensional patterns, Eur. Phys. J. B15, 539-546 (2000).
36. Standish, R. K., On complexity and emergence, Complexity International 9 (2001).
37. Edmonds, B., Hypertext Bibliography of Measures of Complexity, http://bruce.edmonds.name/combib/
38. NECSI Discussion group, http://necsi.org:8100/Lists/complex-science/List.html
39. Latora, V. and Baranger, M., Phys. Rev. Lett. 82, 520 (1999).
40. Gaspard, P. and Wang, X.-J., Phys. Rep. 235, 291 (1993).
41. Aurell, E., Bofetta, G., Crisanti, A., Paladin, G. and Vulpiani, A., Phys. Rev. Lett. 77, 1262 (1996); Abel, M., Biferale, L., Cencini, M., Falcioni, M., Vergni, D. and Vulpiani, A., Physica D147, 12 (2000).
42. Aurell, E., Bofetta, G., Crisanti, A., Paladin, G. and Vulpiani, A., Phys. Rev. Lett. 77, 1262 (1996); Abel, M., Biferale, L., Cencini, M., Falcioni, M., Vergni, D. and Vulpiani, A., Physica D147, 12 (2000).
43. Binder, P.-M. and Plazas, J. A., Phys. Rev. E63, 065203(R) (2001).
44. Bar-Yam, Y., General features of complex systems, UNESCO Encyclopedia of Life Support Systems (in press).
45. Wolf, D. R., Information and correlation in statistical mechanical systems, Ph.D. Dissertation, U. Texas, Austin, Texas, 1996; a quantity discussed here appears to be the same as D(k) though no explicit form was given.
46. Simon, H. A., The Sciences of the Artificial, 3rd Edn. (MIT Press, Cambridge, 1998).
47. Havel, I. M., Scale dimenions in nature, Int. J. General Systems 24, 295 (1996).
48. Auger, P., Dynamics and Thermodynamics in Hierarchically Organized Systems (Pergamon, Oxford, 1990). Auger considers a system subdivided into components and equates the total entropy to a sum of subsystem entropies and entropies of the collective subsystem variables.
49. Cover, T. M. and Thomas, J. A., Elements of Information Theory (Wiley, NY, 1991), p. 12.
50. Mandelbrot, B., The Fractal Geometry of Nature (W. H. Freeman & Co., 1982).
51. Sherrington, D. and Kirkpatrick, S., Phys. Rev. Lett. 35, 1792 (1975).
52. Mattis, D. C., Phys. Lett. 56A, 421 (1976).
53. Gheorghiu-Svirschevski, S. and Bar-Yam, Y., Phys. Rev. E (submitted).
54. Bar-Yam, Y., Complexity rising: From human beings to human civilization, A complexity profile, in Encyclopedia of Life Support Systems (EOLSS), UNESCO (EOLSS Publishers, Oxford, UK, 2004).
55. Bar-Yam, Y., Complexity of military conflict: Multiscale complex systems analysis of littoral warfare, Report to Chief of Naval Operations Strategic Studies Group, 2003.
56. Bar-Yam, Y., Complexity 9, 37-45 (2004).