We present a simple model for the axial dipole moment (ADM) of the geomagnetic field based on a stochastic differential equation for two coupled particles in a biquadratic potential, subjected to Gaussian random perturbations. This model generates aperiodic reversals and excursions separated by stable polarity periods. The model reproduces the temporal asymmetry of geomagnetic reversals, with slower decaying rates before the reversal and faster growing rates after it. This temporal asymmetry is possible because our model is out of equilibrium. The existence of a thermal imbalance between the two particles sets a preferential sense for the energy flux and renders the process irreversible.