On entropy production for controlled Markovian evolution

Journal of Mathematical Physics

Volumn 47, Issue 6, 2006, Pages

  Pavon, Michele ^a   Ticozzi, Francesco ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33745697447     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2207716     Document Type: Article

References (44)

1. Alicki, R., and Lendi, K., Quantum Dynamical Semigroups and Application (Springer-Verlag, New York, 1987).
2. Altafini, C., "Coherent control of open quantum dynamical systems," Phys. Rev. A 70, 062321 (2004).
3. Barron, A., "Entropy and the central limit theorem," Ann. Probab. 14, 336-342 (1986).
4. Braiman, Y., Barhen, J., and Protopopescu, V., "Control of Friction at the Nanoscale," Phys. Rev. Lett. 90, 094301 (2003).
5. Carlen, E. A., and Soffer, A., "Entropy production by block variable summation and central limit theorems," Commun. Math. Phys. 140, 339-371 (1991).
6. Cover, T. M., and Thomas, J. A., Information Theory (Wiley, New York, 1991).
7. Csiszár, I., "Maxent, mathematics and information theory," in Proc. 15th Inter. Workshop on Maximum Entropy and Bayesian Methods, edited by K. M. Hanson and R. N. Silver (Kluver Academic, Dordrecht, 1996), pp. 35-50.
8. Dahleh, M., Pierce, A., Rabitz, H., and Ramakrishna, V., "Control of Molecular Motion," Proc. IEEE 84, 6-15 (1996).
9. Doi, M., and Edwards, S. F., The Theory of Polymer Dynamics (Oxford University Press, New York, 1988).
10. Föllmer, H., in Stochastic Processes - Mathematics and Physics, Lect. Notes in Math. (Springer-Verlag, New York, 1986), Vol. 1158, p. 119.
11. Föllmer, H., "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, pp. 102-203.
12. Georgiou, T., "Spectral analysis based on the state covariance: the maximum entropy spectrum and linear fractional parameterization," IEEE Trans. Autom. Control 47, 1811-1823 (2002).
13. Georgiou, T. T., and Linquist, A., "Kullback-Leibler approximation of spectral density functions," IEEE Trans. Inf. Theory 49, 2910-2917 (2003).
14. Graham, R., "Path integral methods in nonequilibrium thermodynamics and statistics," in Stochastic Processes in Non-equilibrium Systems, edited by L. Garrido, P. Seglar, and P. J. Shepherd, Lecture Notes in Physics (Springer-Verlag, New York, 1978), Vol. 84, pp. 82-138.
15. Haussmann, U. G., and Pardoux, E., "Time reversal of diffusions," Ann. Probab. 14, 1188-1205 (1986).
16. Hernandez, D. B., and Pavon, M., "Equilibrium description of a particle system in a heat bath," Acta Appl. Math. 14, 239-256 (1989).
17. Karatzas, I., and Shreve, S. E., Brownian Motion and Stochastic Calculus (Springer-Verlag, New York, 1988).
18. Kim, K. H., and Qian, H., "Entropy production of Brownian macromolecules with inertia," Phys. Rev. Lett. 93, 120602 (2004).
19. Kullback, S., Information Theory and Statistics (Wiley, New York, 1959).
20. Jaynes, E. T., in Papers on Probability, Statistics and Statistical Physics, edited by R. D. Rosenkranz (Kluwer, Dordrecht, 1983).
21. Le Cam, L., "Convergence of estimates under dimensionality restrictions," Ann. Stat. 1, 38-53 (1973).
22. Ledoux, M., "Logarithmic Sobolev inequalities for unbounded spin systems revisited," Séminaire de Probabilités XXXV, Lecture Notes in Math. (Springer-Verlag, New York, 2001), Vol. 1755, pp. 167-194.
23. Liang, S., Medich, D., Czajkowsky, D. M., Sheng, S., Yuan, J.-Y., and Shao, Z., Ultramicroscopy 84, 119-125 (2000).
24. Lindbald, G., "Completely positive maps and entropy inequalities," Commun. Math. Phys. 40, 147-151 (1975).
25. Morato, L. M., "On the dynamics of diffusions and the related general electromagnetic potentials," J. Math. Phys. 23, 1020-1024 (1982).
26. Nagasawa, M., "The adjoint process of a diffusion with reflecting barrier," Kodai Math. Semin. Rep. 13, 235-248 (1961).
27. Nelson, E., "The adjoint Markov process," Duke Math. J. 25, 671-690 (1958).
28. Nelson, E., Dynamical Theories of Brownian Motion (Princeton University Press, Princeton, NJ, 1967).
29. Nelson, E., Quantum Fluctuations (Princeton University Press, Princeton, NJ, 1985).
30. Nelson, E., "Stochastic mechanics and random fields," 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, pp. 428-450.
31. Nielsen, M. A., and Chuang, I. L., Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2000).
32. Pavon, M., and Ticozzi, F., "Controlling the relative entropy evolution for classical, thermodynamical and quantum systems," Proc. PhysCon 2005 Conf., St. Petersburg, CD-ROM, lSBN:0-7803-9235-3, paper no. 1 (IEEE, New York, 2005), pp. 1-7.
33. Pavon, M., and Ticozzi, F., "Controlling the density evolution of classical, thermodynamic and quantum systems," in the Proc. of 2005 CDC- ECC Conference, Seville, Spain, Dec. 2005, CD-ROM, ISBN/ISSN: 0-9568-9 (IEEE, New York, 2005), pp. 1800-1805.
34. Petz, D., "Entropy, von Neumann and the von Neumann entropy," in John von Neumann and the Foundations of Quantum Physics, edited by M. Redei and M. Stoltzner (Kluwer, Dordrecht, 2001).
35. Qian, H., "Relative entropy: free energy associated with equilibrium fluctuations and nonequilibrium deviations," Phys. Rev. E 63, 042103 (2001).
36. Sakurai, J. J., Modern Quantum Mechanics, revised ed. (Addison-Wesley, New York, 1994).
37. Schumacher, B., and Westmoreland, M. D., "Relative entropy in quantum information theory," in Quantum Information and Quantum Computation: A Millenium Volume, edited by S. J.Lomonaco, Jr. and H. E.Brandt, American Mathematical Society Contemporary Mathematics series (AMS, Providence, R. I., 2001).
38. Schirmer, S. G., Pullen, I. C. H., and Solomon, A. I., "Controllability of Quantum Systems," in Proceedings 2nd IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, edited by A. Astolfi A. Van Der Schaft and F. Gordillo (ISBN 0-08-044278-1) (Elsevier, Sevilla, 2003), pp. 311-316.
39. Spohn, H. "Entropy production for quantum dynamical semigroups," J. Math. Phys. 19, 1227-1230 (1978).
40. Stroock, D., Probability Theory, an Analytic View (Cambridge University Press, New York, 1999).
41. Tamayo, J., Humphris, A. D. L., Owen, R. J., and Miles, M. J., Biophysik 81, 526-537 (2001).
42. Tan, H. N., and Wyatt, J. L., "Thermodynamics of electrical noise in a class of nonlinear RLC networks," IEEE Trans. Circuits Syst. 32, 540-558 (1985).
43. Vedral, V., "The role of relative entropy in quantum information theory," Rev. Mod. Phys. 74, 197-234 (2002).
44. von Neumann, J., Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, NJ, 1955).