Abstract
Fisher information I is a classical concept that originates in estimation theory. Through the Cramer-Rao inequality, it defines the smallest possible error in the estimation of a parameter in the presence of noise obeying a given probability law. More recently, Fisher information has been incorporated within a variational principle for forming the laws of physics (Schrödinger wave equation, Dirac equation, etc.). The premise is that dI / dt ≤ 0, with t the time, so that, at equilibrium, I = min. The premise has recently been proven for any process obeying a Fokker-Planck differential equation. Hence, Fisher information provides a new measure of the passage of time. All errors of estimation increase, on average, with time.
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Frieden, B.R. (1997). Fisher Information as a Measure of Time. In: Tifft, W.G., Cocke, W.J. (eds) Modern Mathematical Models of Time and their Applications to Physics and Cosmology. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5628-8_34
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DOI: https://doi.org/10.1007/978-94-011-5628-8_34
Publisher Name: Springer, Dordrecht
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