Microreversibility and nonequilibrium response theory in magnetic fields

For open systems subjected to external magnetic fields, relations between the statistical cumulants of their fluctuating currents and their response coefficients are established at arbitrary orders in the deviations from equilibrium, as a consequence of microreversibility. These relations are systematically deduced from the extension of the fluctuation relation for this class of systems, and analyzed by using methods developed in Barbier and Gaspard (2018 J. Phys. A: Math. Theor. 51 355001). We unambiguously identify, among the statistical cumulants and their nonequilibrium responses, which of these quantities are left unconstrained by the fluctuation relation, i.e. by microreversibility. We also find the explicit expression of the remaining quantities in terms of the unconstrained ones by means of coefficients of Euler polynomials.