Entropy in stochastic quantum mechanics formulation

L. de la Peña-Auerbach

Takeshi Kodama, Tomoi Koide C

In this note, we discuss the stochastic variational method (SVM) to derive the action principle of Schrödinger equation. In this formalism, the wave function is introduced as one of convenient ways to express the action. This work is a reformulation of Nelson—Yasue’s stochastic quantization scheme and its variational formulation by Yasue, and will furnish possible way to deal with more complicated system such as quantum field theory, suggesting an origin of quantum mechanics.

Ugo Farinelli, A. Gamba

Alberto Barchielli

The theory of measurements continuous in time in quantum mechanics (quantum continual measurements) has been formulated by using the notions of instrument, positive operator valued measure, etc., by using quantum stochastic differential equations and by using classical stochastic differential equations (SDE's) for vectors in Hilbert spaces or for trace-class operators. In the same times Ozawa made developments in the theory of instruments and introduced the related notions of a posteriori states and of information gain [1]. In this paper we introduce a simple class of SDE's relevant to the theory of continual measurements and we recall how they are related to instruments and a posteriori states and, so, to the general formulation of quantum mechanics. Then we introduce and use the notion of information gain and the other results of the paper [1] inside the theory of continual measurements. [1] M. Ozawa, On information gain by quantum measurements of continuous observables, J. Math. Phys. 27 (1986) 759-763.

Vitaly Vanchurin