Controlling the density evolution of classical, thermodynamic and quantum systems

Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

Volumn 2005, Issue , 2005, Pages 1800-1805

  Pavon, Michele ^a   Ticozzi, Francesco ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUUM MECHANICS; ENTROPY; MARKOV PROCESSES; PERTURBATION TECHNIQUES; PROBLEM SOLVING; THERMODYNAMICS;

CLASSICAL MECHANICS; DENSITY EVOLUTION; RELATIVE ENTROPY;

QUANTUM THEORY;

EID: 33745729216     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2005.1582421     Document Type: Conference Paper

References (42)

1. S. Liang, D. Medich, D. M. Czajkowsky, S. Sheng, J. Yuan, and Z. Shao, Ultramicroscopy, 84 (2000), p. 119.
2. K. H. Kim ans H. Qian, "Entropy production of Brownian macromolecules with inertia", Phys. Rev. Lett., 93 (2004), 120602.
3. J. Tamayo, A. D. L. Humphris, R. J. Owen, and M. J. Miles, Biophys., 81 (2001), p. 526.
4. Y. Braiman, J. Barhen, and V. Protopopescu, "Control of Friction at the Nanoscale", Phys. Rev. Lett. 90, (2003), 094301.
5. M. Pavon and F. Ticozzi, On entropy production for controlled Markovian evolution, under preparation.
6. R. M. Murray, Z. Li and S.S. Sastry, A Mathematical Introduction to Robotic Manipulation, CRC Press, Boca Raton, 1994.
7. A. Bloch, J. Baillieul, P. Crouch, and J. Marsden, Nonholonomic Mechanics and Control, Springer Verlag, 2003.
8. M. Dahleh, A.Pierce, H. Rabitz e V. Ramakrishna, Control of Molecular Motion, Proc. IEEE 84 (1996), 6-15.
9. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge Univ. Press, Cambridge, UK, 2000.
10. T. M. Cover and J. A. Thomas, Information Theory Whiley, New York, 1991.
11. R. Graham, Path integral methods in nonequilibrium thermodynamics and statistics, in Stochastic Processes in Nonequilibrium Systems, L. Garrido, P. Seglar and P.J.Shepherd Eds., Lecture Notes in Physics 84, Springer-Verlag, New York, 1978, 82-138.
12. D. Stroock, Probability Theory, an Analytic View, Cambridge University Press, 1999.
13. M. Ledoux, Logarithmic Sobolev inequalities for unbounded spin systems revisited, Séminaire de Probabilités XXXV, Springer-Verlag Lecture Notes in Math. 1755, 167-194.
14. L. Le Cam, Ann. Stat. 1 (1973), p.38.
15. J.C. Willems, Mathematical structures for the study of dynamical phenomena Nieuw Archief voor Wiskunde 4 Volume 1 (1983), 159-192.
16. A.J. van der Schaft, System Theoretic Descriptions of Physical Systems, CWI Tract No. 3, CWI, Amsterdam, 1984.
17. S. Kullback. Information Theory and Statistics, Wiley, 1959.
18. E. T. Jaynes, Papers on Probability, Statistics and Statistical Physics, R.D. Rosenkranz ed., Dordrecht, 1983.
19. I. Csiszár, Maxent, mathematics and information theory, in Proc. 15th Inter. Workshop on Maximum Entropy and Bayesian Methods, K.M. Hanson and R.N. Silver eds., Kluver Academic, 1996, 35-50.
20. T. Georgiou, Spectral analysis based on the state covariance: the maximum entropy spectrum and linear fractional parameterization, IEEE Trans. on Automatic Control, 47(2002), 1811-1823.
21. T. T. Georgiou and A. Linquist, Kullback-Leibler approximation of spectral density functions, IEEE Trans. Inform. Theory, vol.49, pp. 2910-2917, 2003.
22. H. Föllmer, Random fields and diffusion processes, in: Ècole d'Ètè de Probabilitès de Saint-Flour XV-XVII, edited by P. L. Hennequin, Lecture Notes in Mathematics, Springer-Verlag, New York, 1988, vol.1362, 102-203.
23. H. Föllmer, in: Stochastic Processes - Mathematics and Physics , Lect. Notes in Math. 1158 (Springer-Verlag, New York, 1986), p. 119.
24. A. Barron, Entropy and the central limit theorem, Ann. Probab. 14 (1986), 336-342.
25. E. Carlen and A. Soffer, Entropy production by convolution and central limit theorems with strong rate information, Comm. Math. Phys. 140 (1991).
26. D. Petz, Entropy, von Neumann and the von Neumann entropy, in John von Neumann and the Foundations of Quantum Physics, eds. M. Redei and M. Stoltzner, Kluwer, 2001.
27. B. Schumacher and M. D. Westmoreland. Relative entropy in quantum information theory, to appear in Quantum Computation and Quantum Information: A Millenium Volume, S. Lomonaco, editor. American Math. Society Contemporary Mathematics series, 2001.
28. V. Vedral. The role of relative entropy in quantum information theory. Rev. Mod. Phys 74, 197 (2002) .
29. E. Nelson,Dynamical Theories of Brownian Motion, Princeton University Press, Princeton, 1967.
30. E. Nelson, Quantum Fluctuations, Princeton University Press, Princeton, 1985.
31. E. Nelson, The adjoint Markov process, Duke Math. J. 25 (1958), 671.
32. M.Nagasawa, The adjoint process of a diffusion with reflecting barrier, Kodai Math.Sem.Rep. 13, 1961, 235.
33. L. M. Morato, On the dynamics of diffusions and the related general electromagnetic potentials, J. Math. Phys. 23 (1982), 1020.
34. U.G.Haussmann and E.Pardoux, Time reversal of diffusions, The Annals of Probability 14, 1986, 1188.
35. E. Nelson, Quantum Fluctuations, Princeton University Press, Princeton, 1985.
36. M. Pavon and F. Ticozzi, Controlling the relative entropy evolution for classical, thermodynamical and quantum systems, Proc. PhysCon 2005 Conf., St. Petersburg, CD-ROM, ISBN:0-7803-9235-3, paper n. 1, IEEE, 2005, 1-7.
37. J.J. Sakurai. Modern Quantum Mechanics. Addison-Wesley, revised edition, 1994.
38. J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, 1955
39. R. Alicki and K. Lendi. Quantum Dynamical Semigroups and Application. Springer-Verlag, 1987.
40. G. Lindbald. Commun. Math. Phys., 40, 1975.
41. H.M. Wiseman and G.J. Milburn, Quantum theory of optical feedback via homodyne detection, Phys. Rev. Lett., 70, 548, 1993.
42. H.M. Wiseman and S. Mancini, J. Wang, Bayesian feedback versus markovian feedback in a two level atom, Phys. Rev. A, 66, 013807 (2002)