  We demonstrate that in the thermostatted three-dimensional Lorentz gas the
symmetry of the Lyapunov spectrum can be broken by adding to the system an
external magnetic field not perpendicular to the electric field. For
perpendicular field vectors, there is a Hamiltonian reformulation of the
dynamics and the conjugate pairing rule still holds. This indicates that
symmetric Lyapunov spectra has nothing to do with time reversal symmetry or
reversibility; instead, it seems to be related to the existence of a
Hamiltonian connection.
