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Volumn 123, Issue 2, 2006, Pages 315-355

Differential entropy and dynamics of uncertainty

Author keywords

Dynamics of densities; Entropy dynamics; Entropy functionals; Entropy methods; Fisher information; Information localization; Quantum evolution; Shannon entropy; Smoluchowski process; Uncertainty

Indexed keywords


EID: 33646524760     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-006-9058-2     Document Type: Article
Times cited : (52)

References (104)
  • 4
    • 0002042431 scopus 로고    scopus 로고
    • On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations
    • A. Arnold, et al., On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations, Comm. Portia! Diff Equations 26:43-100 (2001).
    • (2001) Comm. Portia! Diff Equations , vol.26 , pp. 43-100
    • Arnold, A.1
  • 5
    • 37649032611 scopus 로고    scopus 로고
    • Upper bound for the time derivative of entropy for nonequilibrium stochastic processes
    • B. C. Bag, Upper bound for the time derivative of entropy for nonequilibrium stochastic processes, Phys. Rev. E 65:046118 (2002).
    • (2002) Phys. Rev. E , vol.65 , pp. 046118
    • Bag, B.C.1
  • 6
    • 0035420120 scopus 로고    scopus 로고
    • Noise properties of stochastic processes and entropy production
    • C. C. Bag, et al., Noise properties of stochastic processes and entropy production, Phys. Rev. E 64:026110 (2001).
    • (2001) Phys. Rev. E , vol.64 , pp. 026110
    • Bag, C.C.1
  • 7
    • 51249188083 scopus 로고
    • Random matrices and information theory
    • R. Balian, Random matrices and information theory, Nuovo Cim. B 57:183-103 (1968).
    • (1968) Nuovo Cim. B , vol.57 , pp. 183-1103
    • Balian, R.1
  • 8
    • 0000061719 scopus 로고
    • Entropy and the central limit theorem
    • A. R. Barron, Entropy and the central limit theorem, Annals Probab. Theory 14:336-342 (1986).
    • (1986) Annals Probab. Theory , vol.14 , pp. 336-342
    • Barron, A.R.1
  • 9
    • 0000898117 scopus 로고
    • Inequalities in Fourier analysis
    • W. Beckner, Inequalities in Fourier analysis, Ann. Math. 102:159-182 (1975).
    • (1975) Ann. Math. , vol.102 , pp. 159-182
    • Beckner, W.1
  • 10
    • 21844520981 scopus 로고
    • On the global existence of Bohmian mechanics
    • K. Berndl, et al., On the global existence of Bohmian mechanics, Commun. Math. Phys. 173:647-673 (1995).
    • (1995) Commun. Math. Phys. , vol.173 , pp. 647-673
    • Berndl, K.1
  • 11
    • 0001040933 scopus 로고
    • Entropie uncertainty relations for angular distributions
    • Białynicki-I. Birula and J. Madajczyk, Entropie uncertainty relations for angular distributions, Phys. Lett. A 108:384-386 (1985).
    • (1985) Phys. Lett. A , vol.108 , pp. 384-386
    • Birula, B.-I.1    Madajczyk, J.2
  • 12
    • 0000617016 scopus 로고
    • Uncertainty relations for information entropy in wave mechanics
    • Białynicki-I. Birula, and J. Mycielski, Uncertainty Relations for Information Entropy in Wave Mechanics, Commun. Math. Phys. 44:129-132 (1975).
    • (1975) Commun. Math. Phys. , vol.44 , pp. 129-132
    • Birula, B.-I.1    Mycielski, J.2
  • 13
    • 0031282806 scopus 로고    scopus 로고
    • Non-negative Feynman-Kac kernels in Schrödinger's interpolation problem
    • Ph. Blanchard and P. Garbaczewski, Non-negative Feynman-Kac kernels in Schrödinger's interpolation problem, J. Math. Phys. 38:1-15 (1997).
    • (1997) J. Math. Phys. , vol.38 , pp. 1-15
    • Blanchard, P.1    Garbaczewski, P.2
  • 14
    • 4243355676 scopus 로고
    • Uncertainty, entropy, and the statistical mechanics of microscopic systems
    • R. Blankenbecler and M. H. Partovi, Uncertainty, entropy, and the statistical mechanics of microscopic systems, Phys. Rev. Lett. 54:373-376 (1985).
    • (1985) Phys. Rev. Lett. , vol.54 , pp. 373-376
    • Blankenbecler, R.1    Partovi, M.H.2
  • 15
    • 0001288577 scopus 로고
    • On the generalization of the Boltzmann H-theorem for a spatially homogeneous Maxwell gas
    • A. V. Bobylev and G. Toscani, On the generalization of the Boltzmann H-theorem for a spatially homogeneous Maxwell gas. J. Math. Phys. 33:2578-2586 (1992).
    • (1992) J. Math. Phys. , vol.33 , pp. 2578-2586
    • Bobylev, A.V.1    Toscani, G.2
  • 16
    • 85009332123 scopus 로고    scopus 로고
    • Trajectory versus probability density entropy
    • M. Bologna, et al., Trajectory versus probability density entropy, Phys. Rev. E 64:016223 (2001).
    • (2001) Phys. Rev. E , vol.64 , pp. 016223
    • Bologna, M.1
  • 18
    • 18344387379 scopus 로고    scopus 로고
    • Conceptual inadequacy of the Shannon information in quantum measurements
    • Ĉ. Brukner and A. Zeilinger, Conceptual inadequacy of the Shannon information in quantum measurements, Phys. Rev. A 63:022113 (2002).
    • (2002) Phys. Rev. A , vol.63 , pp. 022113
    • Brukner, Ĉ.1    Zeilinger, A.2
  • 19
    • 33646535599 scopus 로고    scopus 로고
    • Computation of the entropy of polynomials orthogonal on an interval
    • to appear also math.NA/0310238
    • V. Buyarov, et al., Computation of the entropy of polynomials orthogonal on an interval, SIAM J. Sci. Comp. to appear (2004), also math.NA/0310238.
    • (2004) SIAM J. Sci. Comp.
    • Buyarov, V.1
  • 20
    • 0000273265 scopus 로고
    • Superadditivity of Fisher's information and logarithmic Sobolev inequalities
    • E. A. Carlen, Superadditivity of Fisher's information and logarithmic Sobolev inequalities, J. Funct. Anal. 101:194-211 (1991).
    • (1991) J. Funct. Anal. , vol.101 , pp. 194-211
    • Carlen, E.A.1
  • 21
    • 0001931654 scopus 로고
    • Conservative diffusions
    • E. Carlen, Conservative diffusions, Commun. Math. Phys. 94:293-315 (1984).
    • (1984) Commun. Math. Phys. , vol.94 , pp. 293-315
    • Carlen, E.1
  • 22
    • 41349100418 scopus 로고    scopus 로고
    • Features of the extension of a statistical measure of complexity to continuous systems
    • R. G. Catalan, J. Garay, and Lopez-R. Ruiz, Features of the extension of a statistical measure of complexity to continuous systems, Phys. Rev. E 66:011102 (2002).
    • (2002) Phys. Rev. E , vol.66 , pp. 011102
    • Catalan, R.G.1    Garay, J.2    Ruiz, L.-R.3
  • 23
    • 0000404582 scopus 로고    scopus 로고
    • Quantum information: How much information in a state vector ?
    • C. M. Caves, and C. Fuchs, Quantum information: how much information in a state vector ?. Ann. Israel Phys. Soc. 12:226-237 (1996).
    • (1996) Ann. Israel Phys. Soc. , vol.12 , pp. 226-237
    • Caves, C.M.1    Fuchs, C.2
  • 25
    • 0002121327 scopus 로고
    • Stochastic problems in physics and astronomy
    • S. Chandrasekhar, Stochastic problems in physics and astronomy, Rev. Mod. Phys. 15:1-89 (1943).
    • (1943) Rev. Mod. Phys. , vol.15 , pp. 1-89
    • Chandrasekhar, S.1
  • 26
    • 27644570626 scopus 로고    scopus 로고
    • Information entropy, information distances and complexity of atoms
    • K. Ch. Chatzisavvas, Ch. C., Moustakidis and C. P. Panos, Information entropy, information distances and complexity of atoms. J. Chem. Phys. 123:174111 (2005).
    • (2005) J. Chem. Phys. , vol.123 , pp. 174111
    • Chatzisavvas, K.Ch.1    Moustakidis, Ch.C.2    Panos, C.P.3
  • 29
    • 0037437778 scopus 로고    scopus 로고
    • Frictionless random dynamics: Hydrodynamical formalism
    • R. Czopnik, and P. Garbaczewski, Frictionless Random Dynamics: Hydrodynamical Formalism, Physica A 317:449-471 (2003).
    • (2003) Physica A , vol.317 , pp. 449-471
    • Czopnik, R.1    Garbaczewski, P.2
  • 30
    • 0001677941 scopus 로고    scopus 로고
    • Entropy production and phase space volume contraction
    • D. Daems and G. Nicolis, Entropy production and phase space volume contraction. Phys. Rev. E 59:4000-4006 (1999).
    • (1999) Phys. Rev. E , vol.59 , pp. 4000-4006
    • Daems, D.1    Nicolis, G.2
  • 31
    • 0004685992 scopus 로고    scopus 로고
    • Determining the information flow of dynamical systems from continuous probability distributions
    • G. Deco, et al: Determining the information flow of dynamical systems from continuous probability distributions, Phys. Rev. Lett. 78:2345-2348 (1997).
    • (1997) Phys. Rev. Lett. , vol.78 , pp. 2345-2348
    • Deco, G.1
  • 32
    • 84941428932 scopus 로고
    • Information theoretic inequalities
    • A. Dembo and T. Cover, Information theoretic inequalities, IEEE Trans. Inf. Th. 37:1501-1518 (1991).
    • (1991) IEEE Trans. Inf. Th. , vol.37 , pp. 1501-1518
    • Dembo, A.1    Cover, T.2
  • 33
    • 33749331646 scopus 로고
    • Uncertainty in quantum measurements
    • D. Deutsch, Uncertainty in quantum measurements, Phys. Rev Lett. 50:631-633 (1983).
    • (1983) Phys. Rev Lett. , vol.50 , pp. 631-633
    • Deutsch, D.1
  • 34
    • 26944466817 scopus 로고    scopus 로고
    • Time-dependent entropy of simple quantum systems
    • J. Dunkel and S. A. Trigger, Time-dependent entropy of simple quantum systems, Phys. Rev. A 71:052102 (2005).
    • (2005) Phys. Rev. A , vol.71 , pp. 052102
    • Dunkel, J.1    Trigger, S.A.2
  • 36
    • 0011698814 scopus 로고    scopus 로고
    • Résolution d'un systéme d'équations de M. Schrödingeer
    • 1040
    • R. Fortet, Résolution d'un systéme d'équations de M. Schrödingeer, J. Math. Pures Appl. 9:83 (1040).
    • J. Math. Pures Appl. , vol.9 , pp. 83
    • Fortet, R.1
  • 37
    • 23044440406 scopus 로고
    • Lagrangians of physics and the game of Fisher-information transfer
    • B. R. Frieden and B. H. Sofer, Lagrangians of physics and the game of Fisher-information transfer, Phys. Rev. E 52:2274-2286 (1995).
    • (1995) Phys. Rev. E , vol.52 , pp. 2274-2286
    • Frieden, B.R.1    Sofer, B.H.2
  • 38
    • 0000201728 scopus 로고
    • Some novel characteristics of atomic information entropies
    • S. R. Gadre, et al., Some novel characteristics of atomic information entropies, Phys. Rev. A 32:2602-2606 (1985).
    • (1985) Phys. Rev. A , vol.32 , pp. 2602-2606
    • Gadre, S.R.1
  • 39
    • 0030546566 scopus 로고    scopus 로고
    • Feynman-Kac kernels in Markovian representations of the Schrödinger interpolating dynamics
    • P. Garbaczewski and R. Olkiewicz, Feynman-Kac kernels in Markovian representations of the Schrödinger interpolating dynamics, J. Math. Phys. 37:732-751 (1996).
    • (1996) J. Math. Phys. , vol.37 , pp. 732-751
    • Garbaczewski, P.1    Olkiewicz, R.2
  • 40
    • 3042776760 scopus 로고    scopus 로고
    • Impenetrable barrriers and canonical quantization
    • P. Garbaczewski and W. Karwowski, Impenetrable barrriers and canonical quantization, Am. J. Phys. 72:924-933 (2004).
    • (2004) Am. J. Phys. , vol.72 , pp. 924-933
    • Garbaczewski, P.1    Karwowski, W.2
  • 41
    • 0000195680 scopus 로고    scopus 로고
    • Perturbations of noise: Origins of isothermal flows
    • P. Garbaczewski, Perturbations of noise: Origins of isothermal flows. Phys. Rev. E 59:1498-1511 (1999).
    • (1999) Phys. Rev. E , vol.59 , pp. 1498-1511
    • Garbaczewski, P.1
  • 42
    • 31244434108 scopus 로고    scopus 로고
    • Signatures of randomness in quantum spectra
    • P. Garbaczewski, Signatures of randomness in quantum spectra, Acta Phys. Pol. A 33:1001-1024 (2002).
    • (2002) Acta Phys. Pol. A , vol.33 , pp. 1001-1024
    • Garbaczewski, P.1
  • 43
    • 0034273382 scopus 로고    scopus 로고
    • Stochastic models of exotic transport
    • P. Garbaczewski, Stochastic models of exotic transport, Physica A 285:187-198 (2000).
    • (2000) Physica A , vol.285 , pp. 187-198
    • Garbaczewski, P.1
  • 44
    • 2642553864 scopus 로고    scopus 로고
    • On the (Boltzmann) entropy of non-equilibrium systems
    • S. Goldstein and J. L. Lebowitz, On the (Boltzmann) entropy of non-equilibrium systems, Physica D 193:53-66 (2004).
    • (2004) Physica D , vol.193 , pp. 53-66
    • Goldstein, S.1    Lebowitz, J.L.2
  • 45
    • 0035505261 scopus 로고    scopus 로고
    • Exact uncertainty relations
    • M. J. W. Hall, Exact uncertainty relations, Phys. Rev. A 64:052103 (2001).
    • (2001) Phys. Rev. A , vol.64 , pp. 052103
    • Hall, M.J.W.1
  • 46
    • 0001361646 scopus 로고    scopus 로고
    • Universal geometric approach to uncertainty, entropy and infromation
    • M. J. W. Hall, Universal geometric approach to uncertainty, entropy and infromation, Phys. Rev. A 59: 2602-2615 (1999).
    • (1999) Phys. Rev. A , vol.59 , pp. 2602-2615
    • Hall, M.J.W.1
  • 47
    • 17044404832 scopus 로고
    • Quantum-mechanical histories and the uncertainty principle: Information-theoretic inequalities
    • J. J. Halliwell, Quantum-mechanical histories and the uncertainty principle: Information-theoretic inequalities, Phys. Rev. D 48:2739-2752 (1993).
    • (1993) Phys. Rev. D , vol.48 , pp. 2739-2752
    • Halliwell, J.J.1
  • 48
    • 84980082105 scopus 로고
    • Transmission of information
    • R. V. L. Hartley, Transmission of information, Bell Syst. Techn. J. 7:535-563 (1928).
    • (1928) Bell Syst. Techn. J. , vol.7 , pp. 535-563
    • Hartley, R.V.L.1
  • 49
    • 0038953894 scopus 로고
    • Thermodynamic properties of non-equilibrium states subject to Fokker-Planck equations
    • H. Hasegawa, Thermodynamic properties of non-equilibrium states subject to Fokker-Planck equations. Progr. Theor. Phys. 57:1523-1537 (1977).
    • (1977) Progr. Theor. Phys. , vol.57 , pp. 1523-1537
    • Hasegawa, H.1
  • 50
    • 18344406027 scopus 로고    scopus 로고
    • Steady-state thermodynamics of langevin systems
    • T. Hatano and S. Sasa, Steady-State Thermodynamics of Langevin Systems, Phys. Rev. Lett. 86:3463-3466 (2001).
    • (2001) Phys. Rev. Lett. , vol.86 , pp. 3463-3466
    • Hatano, T.1    Sasa, S.2
  • 51
    • 0001542262 scopus 로고
    • A note on entropy
    • I. I. Hirschman, A note on entropy, Am. J. Math. 79:152-156 (1957).
    • (1957) Am. J. Math. , vol.79 , pp. 152-156
    • Hirschman, I.I.1
  • 52
    • 0000148352 scopus 로고    scopus 로고
    • Quantum chaos of a kicked particle in an infinite potential well
    • B. Hu, et al., Quantum chaos of a kicked particle in an infinite potential well, Phys. Rev. Lett. 82:4224-4227 (1999).
    • (1999) Phys. Rev. Lett. , vol.82 , pp. 4224-4227
    • Hu, B.1
  • 55
    • 11944275853 scopus 로고
    • Information theory and statistical mechanics. II
    • E. T. Jaynes, Information theory and statistical mechanics.II., Phys. Rev. 108:171-190 (1957).
    • (1957) Phys. Rev. , vol.108 , pp. 171-190
    • Jaynes, E.T.1
  • 56
    • 0009447495 scopus 로고
    • Violations of boltzmann's H theorem in real gases
    • E. T. Jaynes, Violations of Boltzmann's H Theorem in Real Gases, Phys. Rev. A 4:747-750 (1971).
    • (1971) Phys. Rev. A , vol.4 , pp. 747-750
    • Jaynes, E.T.1
  • 59
    • 0040120726 scopus 로고    scopus 로고
    • Fluctuation theorem for stochastic dynamics
    • J. Kurchan, Fluctuation theorem for stochastic dynamics, J. Phys. A: Math. Gen. 31:3719-3729 (1998).
    • (1998) J. Phys. A: Math. Gen. , vol.31 , pp. 3719-3729
    • Kurchan, J.1
  • 61
    • 33646522159 scopus 로고    scopus 로고
    • Entropy - A dialogue
    • Eds. A. Grevau, G. Keller, G. Warnecke, Princeton University Press, Princeton
    • J. E. Lebowitz and Ch. Maes, Entropy - a Dialogue, pp. 269-273, in: On Entropy, Eds. A. Grevau, G. Keller, G. Warnecke, Princeton University Press, Princeton, (2003).
    • (2003) On Entropy , pp. 269-273
    • Lebowitz, J.E.1    Maes, Ch.2
  • 62
    • 0000291871 scopus 로고
    • An information-theoretic proof of the central limit theorem
    • Y. V. Linnik, An information-theoretic proof of the central limit theorem, Theory Probab. App. 4:288-299 (1959).
    • (1959) Theory Probab. App. , vol.4 , pp. 288-299
    • Linnik, Y.V.1
  • 63
    • 0001287029 scopus 로고
    • Generalized entropie uncertainty relations
    • H. Maasen and J. B. M. Uffink, Generalized Entropie Uncertainty Relations, Phys. Rev. Lett. 60:1103-1106 (1988).
    • (1988) Phys. Rev. Lett. , vol.60 , pp. 1103-1106
    • Maasen, H.1    Uffink, J.B.M.2
  • 66
    • 0000389761 scopus 로고
    • The dynamic origin of increasing entropy
    • M. C. Mackey, The dynamic origin of increasing entropy, Rev. Mod. Phys. 61, 981-1015 (1989).
    • (1989) Rev. Mod. Phys. , vol.61 , pp. 981-1015
    • Mackey, M.C.1
  • 67
    • 0001434172 scopus 로고    scopus 로고
    • Entropic uncertainty relations for a quantum oscillator
    • V. Majernik and T. Opatrný, Entropic uncertainty relations for a quantum oscillator, J. Phys. A: Math. Gen. 29:2187-2197 (1996).
    • (1996) J. Phys. A: Math. Gen. , vol.29 , pp. 2187-2197
    • Majernik, V.1    Opatrný, T.2
  • 68
    • 0031581765 scopus 로고    scopus 로고
    • Entropie uncertainty relations for the infinite well
    • V. Majernik and L. Richterek, Entropie uncertainty relations for the infinite well, J. Phys. A: Math. Gen. 30: (1997), L49-L54.
    • (1997) J. Phys. A: Math. Gen. , vol.30
    • Majernik, V.1    Richterek, L.2
  • 69
    • 4043141550 scopus 로고    scopus 로고
    • Consistency of the Shannon entropy in quantum experiments
    • P. G. L. Mana, Consistency of the Shannon entropy in quantum experiments, Phys. Rev. A 69:062108 (2004).
    • (2004) Phys. Rev. A , vol.69 , pp. 062108
    • Mana, P.G.L.1
  • 70
    • 0043046816 scopus 로고    scopus 로고
    • Universal property of the information entropy in atoms, nuclei and atomic clusters
    • S. E. Massen and Panos C. P., Universal property of the information entropy in atoms, nuclei and atomic clusters, Phys. Lett. A 246:530-532 (1998).
    • (1998) Phys. Lett. A , vol.246 , pp. 530-532
    • Massen, S.E.1    Panos, C.P.2
  • 71
    • 0036645741 scopus 로고    scopus 로고
    • Universal property of information entropy in fermionic and bosonic systems
    • S. E. Massen, et al., Universal property of information entropy in fermionic and bosonic systems, Phys. Lett. A 299:131-135 (2002).
    • (2002) Phys. Lett. A , vol.299 , pp. 131-135
    • Massen, S.E.1
  • 72
    • 5544246675 scopus 로고    scopus 로고
    • Application of information entropy to nuclei
    • S. E. Massen, Application of information entropy to nuclei, Phys. Rev. C 67:014314 (2003).
    • (2003) Phys. Rev. C , vol.67 , pp. 014314
    • Massen, S.E.1
  • 73
    • 0042756836 scopus 로고
    • Numerical simulations in stochastic mechanics
    • M. McClendon and H. Rabitz, Numerical simulations in stochastic mechanics, Phys. Rev. A 37:3479-3492 (1988).
    • (1988) Phys. Rev. A , vol.37 , pp. 3479-3492
    • McClendon, M.1    Rabitz, H.2
  • 74
    • 0003061577 scopus 로고    scopus 로고
    • Entropy and entropy production in simple stochastic models
    • T. Munakata, A. Igarashi, and T. Shiotani, Entropy and entropy production in simple stochastic models, Phys. Rev. E 57:1403-1409 (1998).
    • (1998) Phys. Rev. E , vol.57 , pp. 1403-1409
    • Munakata, T.1    Igarashi, A.2    Shiotani, T.3
  • 76
    • 1642415051 scopus 로고    scopus 로고
    • What is a state in quantum mechanics?
    • R. G. Newton, What is a state in quantum mechanics?, Am. J. Phys. 72:348-350 (2004).
    • (2004) Am. J. Phys. , vol.72 , pp. 348-350
    • Newton, R.G.1
  • 78
    • 4243703394 scopus 로고
    • Entropie formulation of uncertainty for quantum measurements
    • M. H. Partovi, Entropie formulation of uncertainty for quantum measurements, Phys. Rev. Lett. 50:1883-1885 (1983).
    • (1983) Phys. Rev. Lett. , vol.50 , pp. 1883-1885
    • Partovi, M.H.1
  • 79
    • 0000306754 scopus 로고
    • Universal classification scheme for the spatial-localization properties of one-particle states in finite, d-dimensional systems
    • J. Pipek and I. Varga, Universal classification scheme for the spatial-localization properties of one-particle states in finite, d-dimensional systems, Phys. Rev. A 46:3148-3163 (1992).
    • (1992) Phys. Rev. A , vol.46 , pp. 3148-3163
    • Pipek, J.1    Varga, I.2
  • 80
    • 0036243184 scopus 로고    scopus 로고
    • Thermodynamics of the general diffusion process: Time-reversibility and entropy production
    • H. Qian, M. Qian, and X. Tang, Thermodynamics of the general diffusion process: time-reversibility and entropy production, J. Stat. Phys. 107:1129-1141 (2002).
    • (2002) J. Stat. Phys. , vol.107 , pp. 1129-1141
    • Qian, H.1    Qian, M.2    Tang, X.3
  • 81
    • 41349109494 scopus 로고    scopus 로고
    • Mesoscopic nonequilibrium thermodynamics of single macromolecules and dynamic entropy-energy compensation
    • H. Qian, Mesoscopic nonequilibrium thermodynamics of single macromolecules and dynamic entropy-energy compensation, Phys. Rev. E 65:016102 (2001).
    • (2001) Phys. Rev. E , vol.65 , pp. 016102
    • Qian, H.1
  • 83
    • 0030510906 scopus 로고    scopus 로고
    • Positivity of entropy production in nonequilibrium statistical mechanics
    • D. Ruelle, Positivity of entropy production in nonequilibrium statistical mechanics, J. Stat. Phys. 85:1-23 (1996).
    • (1996) J. Stat. Phys. , vol.85 , pp. 1-23
    • Ruelle, D.1
  • 84
    • 0039377470 scopus 로고    scopus 로고
    • Asymptotic formula for the quantum entropy of position in energy eigenstates
    • J. Sánchez-Ruiz, Asymptotic formula for the quantum entropy of position in energy eigenstates, Phys. Lett. A 226:7-13 (1997).
    • (1997) Phys. Lett. A , vol.226 , pp. 7-13
    • Sánchez-Ruiz, J.1
  • 85
    • 2942555170 scopus 로고    scopus 로고
    • Entropie uncertainty relations for the ground state of a coupled sysytem
    • M. S. Santhanam, Entropie uncertainty relations for the ground state of a coupled sysytem, Phys. Rev. A 69:042301 (2004).
    • (2004) Phys. Rev. A , vol.69 , pp. 042301
    • Santhanam, M.S.1
  • 86
    • 84940644968 scopus 로고
    • A mathematical theory of communication
    • C. E. Shannon, A mathematical theory of communication, Bell Syst. Techn. J. 27:379-423, 623-656 (1948).
    • (1948) Bell Syst. Techn. J. , vol.27 , pp. 379-423
    • Shannon, C.E.1
  • 87
    • 3242784794 scopus 로고    scopus 로고
    • Some observations on the concepts of information-theoretic entropy and randomness
    • J. D. H. Smith, Some observations on the concepts of information- theoretic entropy and randomness, Entropy, 3:1-11 (2001).
    • (2001) Entropy , vol.3 , pp. 1-11
    • Smith, J.D.H.1
  • 88
    • 0035330069 scopus 로고    scopus 로고
    • Information dynamics: Premises, challenges and results
    • K. Sobczyk, Information Dynamics: Premises, Challenges and Results, Mechanical Systems and Signal Processing 15:475-498 (2001).
    • (2001) Mechanical Systems and Signal Processing , vol.15 , pp. 475-498
    • Sobczyk, K.1
  • 89
    • 12944295719 scopus 로고
    • Some inequalities satisfied by the quantities of information of Fisher and Shannon
    • A. J. Stam, Some inequalities satisfied by the quantities of information of Fisher and Shannon, Inf. and Control 2:101-112 (1959).
    • (1959) Inf. and Control , vol.2 , pp. 101-112
    • Stam, A.J.1
  • 90
    • 4444302692 scopus 로고    scopus 로고
    • The information entropy of quantum mechanical states
    • A. Stotland, et al., The information entropy of quantum mechanical states, Europhys. Lett. 67:700-706 (2004).
    • (2004) Europhys. Lett. , vol.67 , pp. 700-706
    • Stotland, A.1
  • 91
    • 0038949574 scopus 로고    scopus 로고
    • Kinetic approach to the asymptotic behaviour of the solution to diffusion equation
    • G. Toscani, Kinetic approach to the asymptotic behaviour of the solution to diffusion equation, Rend, di Matematica Serie VII 16:329-346 (1996).
    • (1996) Rend, di Matematica Serie VII , vol.16 , pp. 329-346
    • Toscani, G.1
  • 92
    • 0030196381 scopus 로고    scopus 로고
    • Maximum entropy principle and non-stationary distributions of stochastic systems
    • J. Trçbicki and K. Sobczyk, Maximum entropy principle and non-stationary distributions of stochastic systems, Probab. Eng. Mechanics 11:169-178 (1996).
    • (1996) Probab. Eng. Mechanics , vol.11 , pp. 169-178
    • Trçbicki, J.1    Sobczyk, K.2
  • 93
    • 29144479501 scopus 로고
    • On the Kullback information measure as a basis for information theory: Comments on a proposal by Hobson and Chang
    • M. Tribus and R. Rossi, On the Kullback information measure as a basis for information theory: Comments on a proposal by Hobson and Chang. J. Stat. Phys. 9:331-338 (1973).
    • (1973) J. Stat. Phys. , vol.9 , pp. 331-338
    • Tribus, M.1    Rossi, R.2
  • 94
    • 26944464193 scopus 로고    scopus 로고
    • Quantum nature of entropy increase for wave packets
    • S. A. Trigger, Quantum nature of entropy increase for wave packets. Bull. Lebedev. Phys. Inst. 9:44-51 (2004).
    • (2004) Bull. Lebedev. Phys. Inst. , vol.9 , pp. 44-51
    • Trigger, S.A.1
  • 95
    • 37649027694 scopus 로고    scopus 로고
    • Rényi entropies characterizing the shape and the extension of the phase-space representation of quantum wave functions in disordered systems
    • I. Varga and J. Pipek, Rényi entropies characterizing the shape and the extension of the phase-space representation of quantum wave functions in disordered systems, Phys. rev. E 68:026202 (2003).
    • (2003) Phys. Rev. E , vol.68 , pp. 026202
    • Varga, I.1    Pipek, J.2
  • 96
    • 0035949664 scopus 로고    scopus 로고
    • Thermodynamics beyond local equilibrium
    • J. M. G. Vilar and J. M. Rubi, Thermodynamics beyond local equilibrium, Proc. Nat. Acad. Sci. (NY) 98:11081-11084 (2001).
    • (2001) Proc. Nat. Acad. Sci. (NY) , vol.98 , pp. 11081-11084
    • Vilar, J.M.G.1    Rubi, J.M.2
  • 97
    • 0009177654 scopus 로고
    • Stochastic opertors, information and entropy
    • J. Voigt, Stochastic opertors, Information and Entropy, Commun. Math. Phys. 81:31-38 (1981).
    • (1981) Commun. Math. Phys. , vol.81 , pp. 31-38
    • Voigt, J.1
  • 98
    • 29144522648 scopus 로고
    • The H-theorem for Boltzmann type equations
    • J. Voigt, The H-Theorem for Boltzmann type equations, J. Reine Angew. Math 326:198-213 (1981).
    • (1981) J. Reine Angew. Math , vol.326 , pp. 198-213
    • Voigt, J.1
  • 99
    • 5844266551 scopus 로고
    • General properties of entropy
    • A. Wehrl, General properties of entropy, Rev. Mod Phys. 50:221-260 (1978).
    • (1978) Rev. Mod Phys. , vol.50 , pp. 221-260
    • Wehrl, A.1
  • 101
    • 0033228877 scopus 로고    scopus 로고
    • Entropic integrals of hyperspherical harmonics and spatial entropy of D-dimensional central potentials
    • R. J. Yañez, et al., Entropic integrals of hyperspherical harmonics and spatial entropy of D-dimensional central potentials, J. Moth. Phys. 40:5675-5686 (1999).
    • (1999) J. Moth. Phys. , vol.40 , pp. 5675-5686
    • Yañez, R.J.1
  • 102
    • 34547109818 scopus 로고
    • Position and information entropies of the D-dimensional harmonic oscillator and hydrogen atom
    • R. J. Yañez, Van W. Assche, J. S. Dehesa, Position and information entropies of the D-dimensional harmonic oscillator and hydrogen atom, Phys. Rev. A 50:3065-3079 (1994).
    • (1994) Phys. Rev. A , vol.50 , pp. 3065-3079
    • Yañez, R.J.1    Van Assche, W.2    Dehesa, J.S.3
  • 104
    • 35949008423 scopus 로고
    • Single- And double-slit diffraction of neutrons
    • A. Zeilinger, et al., Single- and double-slit diffraction of neutrons, Rev. Mod. Phys. 60:1067-1073 (1988).
    • (1988) Rev. Mod. Phys. , vol.60 , pp. 1067-1073
    • Zeilinger, A.1


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