PL EN


Preferences help
enabled [disable] Abstract
Number of results
Journal
2014 | 12 | 3 | 168-174
Article title

Classical analogue of the statistical operator

Content
Title variants
Languages of publication
EN
Abstracts
EN
We advance the notion of a classical density matrix, as a classical analogue of the quantum mechanical statistical operator, and investigate its main properties. In the case of composite systems a partial trace-like operation performed upon the global classical density matrix leads to a marginal density matrix describing a subsystem. In the case of dynamically independent subsystems (that is, non-interacting subsystems) this marginal density matrix evolves locally, its behavior being completely determined by the local phase-space flow associated with the subsystem under consideration. However, and in contrast with the case of ordinary marginal probability densities, the marginal classical density matrix contains information concerning the statistical correlations between a subsystem and the rest of the system.
Publisher
Journal
Year
Volume
12
Issue
3
Pages
168-174
Physical description
Dates
published
1 - 3 - 2014
online
13 - 3 - 2014
References
  • [1] W. H. Zurek (Ed.), Complexity, Entropy, and the Physics of Information (Addison-Wesley, Redwood City, California, 1990)
  • [2] C. Beck, F. Schlogl, Thermodynamics of Chaotic Systems (Cambridge University Press, Cambridge, 1993) http://dx.doi.org/10.1017/CBO9780511524585[Crossref]
  • [3] B. R. Frieden, B. H. Soffer, Phys. Rev. E 42, 2274 (1995) http://dx.doi.org/10.1103/PhysRevE.52.2274[Crossref]
  • [4] B. R. Frieden, Physics from Fisher Information (Cambridge University Press, Cambridge, 1998) http://dx.doi.org/10.1017/CBO9780511622670[Crossref]
  • [5] B. R. Frieden, Science from Fisher Information (Cambridge University Press, Cambridge, 2004) http://dx.doi.org/10.1017/CBO9780511616907[Crossref]
  • [6] H. S. Leff, A. F. Rex (Eds.), Maxwell’s Demons 2: Entropy, Classical and Quantum Information (Institute of Physics Publishing, Bristol, Philadelphia, 2003)
  • [7] N. Margolus, L. B. Levitin, Physica D 120, 188 (1998) http://dx.doi.org/10.1016/S0167-2789(98)00054-2[Crossref]
  • [8] A. Daffertshofer, A. R. Plastino, A. Plastino, Phys. Rev. Lett. 88, 210601 (2002) http://dx.doi.org/10.1103/PhysRevLett.88.210601[Crossref]
  • [9] A. R. Plastino, A. Daffertshofer, Phys. Rev. Lett. 93, 138701 (2004) http://dx.doi.org/10.1103/PhysRevLett.93.138701[Crossref]
  • [10] B. R. Frieden, B. H. Soffer, Phys. Rev. A 74, 052108 (2006) http://dx.doi.org/10.1103/PhysRevA.74.052108[Crossref]
  • [11] M. J. W. Hall, Phys. Rev. A 49, 2602 (1999) http://dx.doi.org/10.1103/PhysRevA.59.2602[Crossref]
  • [12] T. Yamano, Eur. Phys. J. B 86, 363 (2013) http://dx.doi.org/10.1140/epjb/e2013-40634-9[Crossref]
  • [13] V. Giovannetti, S. Lloyd, L. Maccone, Phys. Rev. A 67, 052109 (2003) http://dx.doi.org/10.1103/PhysRevA.67.052109[Crossref]
  • [14] C. Zander, A. R. Plastino, A. Plastino, M. Casas, J. Phys. A: Math. Theor. 40, 2861 (2007) http://dx.doi.org/10.1088/1751-8113/40/11/020[Crossref]
  • [15] A. Borras, C. Zander, A. R. Plastino, M. Casas, A. Plastino, EPL 84, 30007 (2008) http://dx.doi.org/10.1209/0295-5075/81/30007[Crossref]
  • [16] E. T. Jaynes, In: R. D. Rosenkrantz (Ed.), Papers on Probability, Statistics and Statistical Physics (Dordrecht, Reidel, 1987)
  • [17] A. R. Plastino, A. Plastino, Phys. Lett. A 181, 446 (1993) http://dx.doi.org/10.1016/0375-9601(93)91147-W[Crossref]
  • [18] A. R. Plastino, H. G. Miller, A. Plastino, Phys. Rev. E 46, 3927 (1997) http://dx.doi.org/10.1103/PhysRevE.56.3927[Crossref]
  • [19] W. R. Loewenstein, The Touchstone of Life: Molecular Information, Cell Communication, and the Foundations of Life (Oxford University Press, New York, 1999)
  • [20] R. W. Spekkens, Phys. Rev. A 75, 032110 (2007) http://dx.doi.org/10.1103/PhysRevA.75.032110[Crossref]
  • [21] A. R. Plastino, A. Daffertshofer, EPL 84, 30006 (2008) http://dx.doi.org/10.1209/0295-5075/84/30006[Crossref]
  • [22] C. Essex, Planet. Space Sci. 32, 1035 (1984) http://dx.doi.org/10.1016/0032-0633(84)90060-6[Crossref]
  • [23] C. I. Poser, I. C. Sanchez, Macromolecules 14, 370 (1981) http://dx.doi.org/10.1021/ma50003a026[Crossref]
  • [24] O. Vilaseca, L.F. Vega, Fluid Phase Equilibr. 306, 4 (2011) http://dx.doi.org/10.1016/j.fluid.2010.09.018[Crossref]
  • [25] C. Zander, A. R. Plastino, A. Plastino, M. Casas, S. Curilef, Entropy 11, 586 (2009) http://dx.doi.org/10.3390/e11040586[Crossref]
  • [26] L. Susskind, J. Lindesay, An Introduction to Black Holes, Information and the String Theory Revolution: The Holographic Universe (World Scientific Publishing, Singapore, 2005)
  • [27] C. Zander, A. R. Plastino, EPL 86, 18004 (2009) http://dx.doi.org/10.1209/0295-5075/86/18004[Crossref]
  • [28] L. Susskind, The Black Hole War (Back Bay Books, New York, 2008)
  • [29] E. H. Kerner, Gibbs Ensemble, Biological Ensemble (Gordon and Breach, New York, 1972)
  • [30] E. H. Kerner, Phys. Lett. A 151, 401 (1990) http://dx.doi.org/10.1016/0375-9601(90)90911-7[Crossref]
  • [31] Y. Nambu, Phys. Rev. D 7, 2405 (1973) http://dx.doi.org/10.1103/PhysRevD.7.2405[Crossref]
  • [32] A. R. Plastino, A. Plastino, Physica A 232, 458 (1996) http://dx.doi.org/10.1016/0378-4371(96)00140-9[Crossref]
  • [33] R. M. Yamaleev, Ann. Phys. 292, 157 (2001) http://dx.doi.org/10.1006/aphy.2001.6159[Crossref]
  • [34] P. Guha, J. Math. Phys. 43, 4035 (2002) http://dx.doi.org/10.1063/1.1481955[Crossref]
  • [35] A. R. Plastino, A. Plastino, L. R. da Silva, M. Casas, Physica A 271, 343 (1999) http://dx.doi.org/10.1016/S0378-4371(99)00217-4[Crossref]
  • [36] G. Roston, A. R. Plastino, M. Casas, A. Plastino, L. R. da Silva, Eur. Phys. J. B 48, 87 (2005) http://dx.doi.org/10.1140/epjb/e2005-00372-3[Crossref]
  • [37] S. Mongkolsakulvong, P. Chaikhan, T.D. Frank, Eur. Phys. J. B 85, 90 (2012) http://dx.doi.org/10.1140/epjb/e2012-20720-4[Crossref]
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-014-0438-y
Identifiers
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.