Question about Noether's Theorem.

[lugita15]

According to Noether's Theorem, for every symmetry of the Lagrangian there is a corresponding conservation law. For instance, the invariance of the Lagrangian under time translation and space translation correspond to the conservation laws of energy and momentum, respectively. Also, the invariance of the Lagrangian under rotation in space corresponds to the conservation of angular momentum.

In classical mechanics at least, the laws of physics are also T-symmetric, i.e. they are symmetric with respect to time reversal. What is the corresponding conserved quantity, and how is it derived from the Lagrangian?

Any help would be greatly appreciated.
Thank You in Advance.

 

[Rainbow Child]

Noether's Theorem talks about continuous groups of transformations.

The time reversal is a discrete group$$^1$$ of transformations, thus it does not corresponds to any conservation law.


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$$^1$$ Along with the identity transformation of course.