Fisher information and semiclassical treatments

Entropy

Volumn 11, Issue 4, 2009, Pages 972-992

  Pennini, Flavia ^a,b   Ferri, Gustavo ^c   Plastino, Angelo ^b  

^a UNIVERSIDAD CATÓLICA DEL NORTE   (Chile)

^b INSTITUTO DE FÍSICA LA PLATA   (Argentina)

^c UNIVERSIDAD NACIONAL DE LA PAMPA   (Argentina)

Author keywords

Delocalization; Fisher measures; Information theory; Phase space; Purity; Semiclassical information; Thermal uncertainties

Indexed keywords

EID: 77949568175     PISSN: None     EISSN: 10994300     Source Type: Journal    
DOI: 10.3390/e11040972     Document Type: Letter

References (42)

1. Frieden, B.R. Science from Fisher Information, 2nd ed.; Cambridge University Press: Cambridge, UK, 2004.
2. Wootters, W.K. The acquisition of information from quantum measurements. PhD Dissertation, University of Texas, Austin, TX, USA, 1980.
3. Frieden, B.R.; Soffer, B.H. Lagrangians of physics and the game of Fisher-information transfer. Phys. Rev. E 1995, 52, 2274-2286.
4. Pennini, F.; Plastino, A.R.; Plastino, A. Rènyi entropies and Fisher informations as measures of nonextensivity in a Tsallis setting. Physica A 1998, 258, 446-457.
5. Frieden, B.R.; Plastino, A.; Plastino, A.R.; Soffer, H. Fisher-based thermodynamics: Its Legendre transformations and concavity properties. Phys. Rev. E 1999, 60, 48-53.
6. Pennini, F.; Plastino, A.; Plastino, A.R.; Casas, M. How fundamental is the character of thermal uncertainty relations? Phys. Lett. A 2002, 302, 156-162.
7. Plastino, A.R.; Plastino, A. Symmetries of the Fokker-Planck equation and the Fisher-Frieden arrow of time. Phys. Rev. E 1996, 54, 4423-4426.
8. Plastino, A.; Plastino, A.R.; Miller, H.G. On the relationship between the Fisher-Frieden-Soffer arrow of time, and the behaviour of the Boltzmann and Kullback entropies. Phys. Lett. A 1997, 235, 129-134.
9. Anderson, A.; Halliwell, J.J. Information-theoretic measure of uncertainty due to quantum and thermal fluctuations. Phys. Rev. D 1993, 48, 2753-2765.
10. Dimassi, M.; Sjoestrand, J. Spectral Asymptotics in the Semiclassical Limit; Cambridge Univesity Press: Cambridge, UK, 1999.
11. Brack, M.; Bhaduri, R.K. Semiclassical Physics; Addison-Wesley: Boston, MA, USA, 1997.
12. Wehrl, A. On the relation between classical and quantum entropy. Rep. Math. Phys. 1979, 16, 353-358.
13. Lieb, E.H. Proof of an entropy conjecture of wehrl. Commun. Math. Phys. 1978, 62, 35-41.
14. Schnack, J. Thermodynamics of the harmonic oscillator using coherent states. Europhys. Lett. 1999, 45, 647-652.
15. Klauder, J.R.; Skagerstam, B.S. Coherent States; World Scientific: Singapore, 1985.
16. Pathria, R.K. Statistical Mechanics; Pergamon Press: Exeter, UK, 1993.
17. Pennini, F.; Plastino, A. Heisenberg-Fisher thermal uncertainty measure. Phys. Rev. E 2004, 69, 057101:1-57101:4.
18. Wigner, E.P. On the quantum correction for thermodynamic equilibrium. Phys. Rev. 1932, 40, 749-759.
19. Wlodarz, J.J. Entropy and wigner distribution functions revisited. Int. J. Theor. Phys. 2003, 42, 1075-1084.
20. Husimi, K. Some formal properties of the density matrix. Proc. Phys. Math. Soc. JPN 1940, 22, 264-283.
21. O' Connel, R.F.; Wigner, E.P. Some properties of a non-negative quantum-mechanical distribution function. Phys. Lett. A 1981, 85, 121-126.
22. Mizrahi, S.S. Quantum mechanics in the Gaussian wave-packet phase space representation. Physica A 1984, 127, 241-264.
23. Mizrahi, S.S. Quantum mechanics in the Gaussian wave-packet phase space representation II: Dynamics. Physica A 1986, 135, 237-250.
24. Mizrahi, S.S. Quantum mechanics in the gaussian wave-packet phase space representation III: From phase space probability functions to wave-functions. Physica A 1988, 150, 541-554.
25. Pennini, F.; Plastino, A. Escort Husimi distributions, Fisher information and nonextensivity. Phys. Lett. A 2004, 326, 20-26.
26. Cramer, H. Mathematical Methods of Statistics; Princeton University Press: Princeton, NJ, USA, 1946.
27. Rao, C.R. Information and accuracy attainable in the estimation of statistical parameters. Bull. Calcutta Math. Soc. 1945, 37, 81-91.
28. Jaynes, E.T. Information theory and statistical mechanics I. Phys. Rev. 1957, 106, 620-630.
29. Jaynes, E.T. Information theory and statistical mechanics II. Phys. Rev. 1957, 108, 171-190.
30. Jaynes, E.T. Papers on Probability, Statistics and Statistical Physics; Rosenkrantz, R.D., Ed.; Kluwer Academic Publishers: Norwell, MA, USA, 1987.
31. Katz, A. Principles of Statistical Mechanics: The Information Theory Approach: Freeman and Co.: San Francisco, CA, USA, 1967.
32. Sugita, A.; Aiba, H. Second moment of the Husimi distribution as a measure of complexity of quantum states. Phys. Rev. E 2002, 65, 36205:1-36205:10.
33. Mandelbrot, B. The role of sufficiency and of estimation in thermodynamics. Ann. Math. Stat. 1962, 33, 1021-1038.
34. Pennini, F.; Plastino, A. Power-law distributions and Fisher's information measure. Physica A 2004, 334, 132-138.
35. Dodonov, V.V. Purity- and entropy-bounded uncertainty relations for mixed quantum states. J. Opt. B Quantum Semiclass. Opt. 2002, 4, S98-S108.
36. Munro, W.J.; James, D.F.V.; White, A.G.; Kwiat, P.G. Maximizing the entanglement of two mixed qubits. Phys. Rev. A 2003, 64, 30302:1-30302:4.
37. Fano, U. Description of states in quantum mechanics by density matrix and pperator techniques. Rev. Mod. Phys. 1957, 29, 74-93.
38. Batle, J.; Plastino, A.R.; Casas, M.; Plastino, A. Conditional q-entropies and quantum separability: A numerical exploration. J. Phys. A Math. Gen. 2002, 35, 10311-11324.
39. Anderson, M.H.; Ensher, J.R.; Matthews, M.R.; Wieman, C.E.; Cornell, E.A. Observation of bose-einstein condensation in a dilute atomic vapor. Science 1995, 269, 198-201.
40. Davis, K.B.; Mewes, M.-O.; Andrews, M.R.; van Druten, N.J.; Durfee, D.S.; Kurn, D.M.; Ketterle, W. Bose-einstein condensation in a gas of sodium atoms. Phys. Rev. Lett. 1995, 75, 3969-3973.
41. Bradley, C.C.; Sackett, C.A.; Hulet, R.G. Bose-einstein condensation of lithium: Observation of limited condensate number. Phys. Rev. Lett. 1997, 78, 985-989.
42. Curilef, S.; Pennini, F.; Plastino, A.; Ferri, G.L. Fisher information, delocalization and the semiclassical description of molecular rotation. J. Phys. A Math. Theor. 2007, 40, 5127-5140.