Entropy and Wigner Distribution Functions Revisited

Several expressions for quantum entropy proposed in the literature are evaluated within the Weyl—Wigner—Moyal phase-space representation of quantum mechanics, with emphasis on some important subtle points in this approach. It has been found that the Rényi—Süßmann entropy and its linearization are distinguished because of their properties.

[1]  J. Wlodarz Self‐dual phase‐space representation of quantum mechanics and the variational principle , 1994 .

[2]  N. Balazs Weyl's association, Wigner's function and affine geometry , 1980 .

[3]  Modeling the reversible decoherence of mesoscopic superpositions in dissipative environments , 2001, quant-ph/0106044.

[4]  J. Wlodarz On phase-space representations of quantum mechanics , 2001 .

[5]  E. Wigner On the quantum correction for thermodynamic equilibrium , 1932 .

[6]  Nonlocality of the Einstein-Podolsky-Rosen state in the phase space , 1999, quant-ph/9904071.

[7]  A. Voros,et al.  An algebra of pseudodifferential operators and the asymptotics of quantum mechanics , 1978 .

[8]  M. Nemes,et al.  QUANTUM DYNAMICAL MANIFESTATION OF CHAOTIC BEHAVIOR IN THE PROCESS OF ENTANGLEMENT , 1998 .

[9]  Konrad Banaszek,et al.  TESTING QUANTUM NONLOCALITY IN PHASE SPACE , 1999 .

[10]  A. Wehrl On the relation between classical and quantum-mechanical entropy , 1979 .

[11]  Geometrical evaluation of star products , 1999, hep-th/9912238.

[12]  Habib,et al.  Coherent states via decoherence. , 1993, Physical review letters.

[13]  J. Bell,et al.  EPR Correlations and EPW Distributions , 1986 .

[14]  E. Gyftopoulos,et al.  Entropy: Thermodynamic definition and quantum expression , 1997 .

[15]  G. Patil,et al.  Diversity as a Concept and its Measurement , 1982 .

[16]  Caslav Brukner,et al.  OPERATIONALLY INVARIANT INFORMATION IN QUANTUM MEASUREMENTS , 1999 .

[17]  J. Wlodarz On marginalization of phase-space distribution functions , 1999 .

[18]  On one controversy about the smoothed Wigner function , 1992 .

[19]  W. Thirring Lehrbuch der Mathematischen Physik , 1977 .

[20]  H. Toutenburg Rnyi, A.: Probability Theory. Akadmiai Kiad, Budapest 1970. 666 S , 1971 .

[21]  Decoherence versus entropy in neutron interferometry , 1999, quant-ph/9906118.

[22]  U. Sen,et al.  Mixedness in the Bell violation versus entanglement of formation , 2001, quant-ph/0104007.

[23]  L. G. Suttorp,et al.  Foundations of electrodynamics , 1972 .

[24]  Berry phase due to quantum measurements , 1999, quant-ph/9904082.

[25]  Satosi Watanabe,et al.  Über die Anwendung thermodynamischer Begriffe auf den Normalzustand des Atomkerns , 1939 .

[26]  M. Scully,et al.  Distribution functions in physics: Fundamentals , 1984 .

[27]  M. Carolina Nemes,et al.  Recoherence in the entanglement dynamics and classical orbits in the N-atom Jaynes-Cummings model , 2001 .

[28]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[29]  A. Wehrl General properties of entropy , 1978 .

[30]  On the relation between classical and quantum-thermodynamic entropy , 1984 .

[31]  DEFORMATION QUANTIZATION: QUANTUM MECHANICS LIVES AND WORKS IN PHASE-SPACE , 2001, hep-th/0110114.

[32]  Jean-Pierre Vigier,et al.  A review of extended probabilities , 1986 .

[33]  Lars M. Johansen EPR correlations and EPW distributions revisited , 1997 .

[34]  B. K. Jennings,et al.  Wigner's function and other distribution functions in mock phase spaces , 1984 .

[35]  Berry phase for many-spin system with the uniaxial anisotropic exchange interaction in a time-dependent magnetic field , 2002 .

[36]  A note on the wigner distribution function , 1988 .

[37]  C. Zachos,et al.  Features of time-independent Wigner functions , 1997, hep-th/9711183.

[38]  C. Tsallis Possible generalization of Boltzmann-Gibbs statistics , 1988 .

[39]  R. Estrada,et al.  On asymptotic expansions of twisted products , 1989 .

[40]  Manfredi,et al.  Entropy and wigner functions , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[41]  J. P. Dahl Dynamical Equations for the Wigner Functions , 1983 .

[42]  O. Cohen Nonlocality of the original Einstein-Podolsky-Rosen state , 1997 .