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