Heat exchanges in a quenched ferromagnet

The off-equilibrium probability distribution of the heat exchanged by a ferromagnet in a time interval after a quench below the critical point is calculated analytically in the large-N limit. The distribution is characterized by a singular threshold QC < 0, below which a macroscopic fraction of heat is released by the k = 0 Fourier component of the order parameter. The mathematical structure producing this phenomenon is the same responsible for the order parameter condensation in the equilibrium low temperature phase. The heat exchanged by the individual Fourier modes follows a non-trivial pattern, with the unstable modes at small wave vectors warming up the modes around a characteristic finite wave vector kM. Two internal temperatures, associated with the k = 0 and k = kM modes, rule the heat currents through a fluctuation relation similar to the one for stationary systems in contact with two thermal reservoirs.