The validity of the fluctuation relations (FRs) for systems in a constant magnetic field is investigated. Recently introduced time-reversal symmetries that hold in the presence of static electric and magnetic fields and of deterministic thermostats are used to prove the transient FRs without invoking, as commonly done, inversion of the magnetic field. Steady-state FRs are also derived, under the $t$-mixing condition. These results extend the predictive power of important statistical mechanics relations. We illustrate this via the nonlinear response for the cumulants of the dissipation, showing how the alternative FRs enable one to determine analytically null cumulants also for systems in a single magnetic field.

• Received 11 May 2020
• Revised 26 July 2020
• Accepted 5 August 2020

DOI:https://doi.org/10.1103/PhysRevE.102.030101