Abstract
We propose an “informational time” concerning some stochastic dynamical systems where there is an uncertainty on the state of the system or the space localization of a phenomenon. In each case the informational time is defined by the increase of a Shannon's informational entropy, formulated either exactly or asymptotically or in the case of Laplace-Gauss probability densities. After giving some remarks on Shannon's informational entropy, three examples are considered: a linear differential system with uncertain initial state, a “stochastic systemswith diffusion”, and a quantum system. The informational times proposed are expressed, in terms of classical time t, by the integral of a positive function of t, the logarithm of the square root of t and the logarithm of t.
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References
A.Erdélyi: Asymptotic Expansion.New York:Dover 1956
G.Jumarie: Extension of quantum information by using entropy of de terministic functions.Mathematical and Computer Modelling, 15. 103–116 (1991)
A.Messiah: Mécanique Quantique I.Paris:Dunod 1959
R. Vallée:Expression asymptotique, pour les grandes valeurs, dn temps de l'information associée à la fonction d'ondes dans le cas d'un corpuscule libre. Comptes rendus de l'Académie des Sciences, B, 267, 529–532 (1968)
R. Vallée: Aspect informationnel du problème de la prévision dans le cas d'une observation initiale imparfaite.Economie Appliquée, 32,2.3 221–227 (1979)
R.Vallée:Evolution of a dynamical linear, system, with random initial conditions. In:R.Trappl (ed.): Cybernetics and Systems Research. Amsterdam:North Holland Publishing Company 1982, pp.163–164
R.Vallée: Information entropy and state observation of a dynamical system.In: B.Bouchon, R.R. Yager (eds.): Uncertainty in. Knowledge Ba sed Systems.Berlin:Springer-Verlag 1987,pp.403–405
R.Vallée: Information and Schrödinger's equation.SCIMA Systems and Cybernetics in Management, 20,3,71–75 (1991)
R.Vallée: The “epsilon-distribution” or the antithesis of Dirac delta. In:R.Trappl (ed.): Cybernetics and Systems Research'92. Singapore: World Scientific 1992,pp.97–102
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© 1995 Springer-Verlag Berlin Heidelberg
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Vallée, R. (1995). Informational time. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (eds) Advances in Intelligent Computing — IPMU '94. IPMU 1994. Lecture Notes in Computer Science, vol 945. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035958
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DOI: https://doi.org/10.1007/BFb0035958
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