Kolmogorov--Sinai entropy for p-preserving systems
-
Mona Khare
Abstract
The objective of the present paper is to develop a comprehensive theory of entropy in the realm of a gs-space
Funding source: Council of Scientific and Industrial Research
Award Identifier / Grant number: 09/001(0320)/2009-EMR-I
Funding statement: The second author acknowledges financial support by Council of Scientific and Industrial Research (CSIR), New Delhi (India), under grant no. 09/001(0320)/2009-EMR-I.
Acknowledgements
We would like to express our gratitude to the anonymous referee for careful reading of the manuscript and valuable suggestions that improved the readability of the manuscript.
References
[1] L. Beran, Orthomodular Lattices, Math. Appl. (East European Series), D. Reidel Publishing, Dordrecht, 1985. 10.1007/978-94-009-5215-7Suche in Google Scholar
[2] G. Birkhoff and J. von Neumann, The logic of quantum mechanics, Ann. of Math. (2) 37 (1936), no. 4, 823–843. 10.2307/1968621Suche in Google Scholar
[3] B. De Baets and R. Mesiar, T-partitions, Fuzzy Sets and Systems 97 (1998), no. 2, 211–223. 10.1016/S0165-0114(96)00331-4Suche in Google Scholar
[4] E. Kagan and I. Ben-Gal, Navigation of quantum-controlled mobile robots, Recent Advances in Mobile Robotics, InTech, Shanghai (2011), 311–326. 10.5772/25944Suche in Google Scholar
[5] G. Kalmbach, Orthomodular Lattices, London Math. Soc. Monogr. Ser. 18, Academic Press, London, 1983. Suche in Google Scholar
[6] M. Khare and S. Roy, Conditional entropy and the Rokhlin metric on an orthomodular lattice with Bayessian state, Internat. J. Theoret. Phys. 47 (2008), no. 5, 1386–1396. 10.1007/s10773-007-9581-1Suche in Google Scholar
[7] M. Khare and S. Roy, Entropy of quantum dynamical systems and sufficient families in orthomodular lattices with Bayesian state, Commun. Theor. Phys. (Beijing) 50 (2008), no. 3, 551–556. 10.1088/0253-6102/50/3/02Suche in Google Scholar
[8] M. Khare, B. Singh and A. Shukla, Relative entropy and mutual information on a quantum logic, Math. Aeterna 3 (2013), no. 7–8, 555–563. Suche in Google Scholar
[9] A. Khrennikov, Non-Kolmogorov probability models and modified Bell’s inequality, J. Math. Phys. 41 (2000), no. 4, 1768–1777. 10.1063/1.533210Suche in Google Scholar
[10] A. Khrennikov, Contextual Approach to Quantum Formalism, Fundam. Theor. Phys. 160, Springer, New York, 2009. 10.1007/978-1-4020-9593-1Suche in Google Scholar
[11] O. Nánásiová, Map for simultaneous measurements for a quantum logic, Internat. J. Theoret. Phys. 42 (2003), no. 9, 1889–1903. 10.1023/A:1027384132753Suche in Google Scholar
[12] B. Riečan, Kolmogorov–Sinaj entropy on MV-algebras, Internat. J. Theoret. Phys. 44 (2005), no. 7, 1041–1052. 10.1007/s10773-005-7080-9Suche in Google Scholar
[13] H.-J. Yuan, Entropy of partitions on quantum logic, Commun. Theor. Phys. (Beijing) 43 (2005), no. 3, 437–439. 10.1088/0253-6102/43/3/012Suche in Google Scholar
[14] Y.-X. Zhao and Z.-H. Ma, Conditional entropy of partitions on quantum logic, Commun. Theor. Phys. (Beijing) 48 (2007), no. 1, 11–13. 10.1088/0253-6102/48/1/003Suche in Google Scholar
© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- A priori error analysis of the implicit Euler, spectral discretization of a nonlinear equation for a flow in a partially saturated porous media
- Sharp geometric requirements in the Wachspress interpolation error estimate
- Kolmogorov--Sinai entropy for p-preserving systems
- A note on the relation between categories and hyperstructures
- On generalized Sasakian-space-forms with M-projective curvature tensor
Artikel in diesem Heft
- Frontmatter
- A priori error analysis of the implicit Euler, spectral discretization of a nonlinear equation for a flow in a partially saturated porous media
- Sharp geometric requirements in the Wachspress interpolation error estimate
- Kolmogorov--Sinai entropy for p-preserving systems
- A note on the relation between categories and hyperstructures
- On generalized Sasakian-space-forms with M-projective curvature tensor
