Fluctuation relations for dissipative systems in constant external magnetic field: theory and molecular dynamics simulations

It has recently been pointed out that Hamiltonian particle systems in constant magnetic fields satisfy generalized time-reversal symmetries that enable to prove useful statistical relationships based on equilibrium phase-space probability distributions without the need to invert, as commonly considered necessary, the magnetic field. Among these relations, that hold without need of Casimir modifications, one finds the standard linear response Green-Kubo relations, and consequently the Onsager reciprocal relations. Going beyond linear response is also possible, for instance in terms of transient and steady state Fluctuation Relations (FRs). Here we highlight how the generalized time-reversal symmetries ensure that the (transient) FRs theory directly applies also for systems in external magnetic fields. Furthermore we show that transient FR can indeed be verified in nonequilibrium molecular dynamics simulations, for systems subjected to magnetic and electric fields, which are thermostatted \`a la Nos\'e-Hoover. The result is nontrivial because, since it is not immediate within which sizes and time scales the effects can actually be observable, it is not obvious what one may obtain by real molecular dynamics simulations.