  Microreversibility constrains the fluctuations of the nonequilibrium currents
that cross an open system. This can be seen from the so-called fluctuation
relations, which are a direct consequence of microreversibility. Indeed, the
latter are known to impose time-reversal symmetry relations on the statistical
cumulants of the currents and their responses at arbitrary orders in the
deviations from equilibrium. Remarkably, such relations have been recently
analyzed by means of Euler's polynomials. Here we show that fluctuation
relations can actually be explicitly written in terms of the constant terms of
these particular polynomials. We hence demonstrate that Euler's polynomials are
indeed fundamentally rooted in fluctuation relations, both in the absence and
the presence of an external magnetic field.
