A Stochastic Version of the Noether Theorem

A stochastic version of the Noether theorem is derived for systems under the action of external random forces. The concept of moment generating functional is employed to describe the symmetry of the stochastic forces. The theorem is applied to two kinds of random covariant forces. One of them genera...

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Bibliographic Details
Published in:Foundations of physics 2018-06, Vol.48 (6), p.726-746
Main Authors: González Lezcano, Alfredo, Cabo Montes de Oca, Alejandro
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Classical Mechanics
History and Philosophical Foundations of Physics
Philosophy of Science
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Statistical Physics and Dynamical Systems
Theorems
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Summary:A stochastic version of the Noether theorem is derived for systems under the action of external random forces. The concept of moment generating functional is employed to describe the symmetry of the stochastic forces. The theorem is applied to two kinds of random covariant forces. One of them generated in an electrodynamic way and the other is defined in the rest frame of the particle as a function of the proper time. For both of them, it is shown the conservation of the mean value of a random drift momentum. The validity of the theorem makes clear that random systems can produce causal stochastic correlations between two faraway separated systems, that had interacted in the past. In addition possible connections of the discussion with the Ives Couder’s experimental results are remarked.
ISSN:0015-9018
1572-9516
DOI:10.1007/s10701-018-0174-z