Time reversal symmetry for classical, non-relativistic quantum and spin systems in presence of magnetic fields

We extend to quantum mechanical systems results previously obtained for classical mechanical systems, concerning time reversibility in presence of a magnetic field. As in the classical case, results like the Onsager reciprocal relations and the so-called fluctuation theorems, are consequently obtained, without recourse to the Casimir modification. The quantum systems treated here are non-relativistic, and are described by the Schrödinger equation or the Pauli equation. In particular, we prove that the spin-field interaction does not break the time reversal invariance (TRI) of the dynamics, and that it does not require additional conditions for such a symmetry to hold, compared to the spinless cases. These results are relevant for experiments such as diffusion in solutions, thermoelectricity and spin charge transport. Indeed, no violation of the Onsager relations has been found in presence of a magnetic field, contrary to general expectations.