Maximum Shannon entropy, minimum Fisher information, and an elementary game

Foundations of Physics

Volumn 32, Issue 11, 2002, Pages 1757-1772

  Luo, Shunlong ^a,b  

^a INSTITUTE OF APPLIED MATHEMATICS   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Binary probability; Fisher information; Game against nature; Malus' law; Shannon entropy

Indexed keywords

EID: 0036961426     PISSN: 00159018     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021454807474     Document Type: Article

References (24)

1. W. Yourgrau and S. Mandelstam, Variational Principles in Dynamics and Quantum Theory, 2nd edn. (Pitman, London, 1960).
2. J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton University Press, New Jersey, 1955).
3. E. T. Jaynes, "Information theory and statistical mechanics, I & II," Phys. Rev. 106, 620-630(1957); 108, 171-190 (1957).
4. E. T. Jaynes, "Information theory and statistical mechanics, I & II," Phys. Rev. 106, 620-630(1957); 108, 171-190 (1957).
5. C. Brukner and A. Zeilinger, "Conceptual inadequacy of the Shannon information in quantum measurements," Phys. Rev. A 63, 022113, 1-10 (2001).
6. B. R. Frieden and B. H. Soffer, "Lagrangians of physics and the game of Fisher-information transfer," Phys. Rev. E 52, 2274-2286 (1995).
7. B. R. Frieden, Physics from Fisher Information: A Unification (Cambridge University Press, 1998).
8. R. A. Fisher, "Theory of statistical estimation," Proc. Camb. Phil. Soc. 22, 700-725 (1925).
9. J. H. Wheeler, "Information, physics, quantum: the search of links," in Complexity, Entropy, and Physics of Information, Z. H. Zurek, ed. (Addison-Wesley, Reading, MA, 1990), pp. 3-28.
10. J. Summhammer, "Maximum predictive power and the superposition principle," Int. J. Theor. Phys. 33, 171-178 (1994).
11. J. Summhammer, "Structure of probabilistic information and quantum laws," arXiv: quant-ph/0102099, contribution to conference Foundations of Probability and Physics, Vaxjo University, Sweden, 27 Nov.-1 Dec. 2000.
12. A. Zeilinger, "A foundational principle for quantum mechanics," Found. Phys. 29, 631-643 (1999).
13. C. Brukner and A. Zeilinger, "Malus' law and quantum information," Acta Physica Slovaca, 49, 647-652 (1999).
14. N. Wiener, Cybernetics (MIT Press, Cambridge, MA, 1948).
15. C. E. Shannon and W. Weaver, The Mathematical Theory of Communication (University of Illinois Press, Urbana, 1949).
16. L. Brillouin, Science and Information (Academic, New York, 1956).
17. L. Szilard, "Über die Entropieverminderung in einem thermodynamischen System bei eingriffen intelligenter wesen," Z. Phys. 53, 840-856 (1929) (an English translation appeared in Behavioral Sci. 9, 301-310 (1964)).
18. L. Szilard, "Über die Entropieverminderung in einem thermodynamischen System bei eingriffen intelligenter wesen," Z. Phys. 53, 840-856 (1929) (an English translation appeared in Behavioral Sci. 9, 301-310 (1964)).
19. J. Hilgevoord and J. B. M. Uffink, "The mathematical expression of the uncertainty principle," in Microphysical Reality and Quantum Formalism, A. van der Merwe et al., eds. (Kluwer Academic, Dordrecht, 1988), pp. 91-114.
20. S. L. Luo, "Fisher information matrix of Husimi distribution," J. Stat. Phys. 102, 1417-1428 (2001).
21. H. Cramér, Mathematical Methods of Statistics (Princeton University Press, Princeton, 1946).
22. T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, New York, 1991).
23. P. A. M. Dirac, The Principles of Quantum Mechanics, 4th edn. (Clarendon, Oxford, 1958).
24. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, Vol. III (Addison-Wesley, Reading, MA, 1965).