Macroscopic time-reversal symmetry breaking at a nonequilibrium phase transition

We study the entropy production in a globally coupled Brownian particles system that undergoes an order-disorder phase transition. Entropy production is a characteristic feature of nonequilibrium dynamics with broken detailed balance. We find that the entropy production rate is subextensive in the disordered phase and extensive in the ordered phase. It is found that the entropy production rate per particle vanishes in the disordered phase and becomes positive in the ordered phase following critical scaling laws. We derive the scaling relations for associated critical exponents. The disordered phase exemplifies a case where the entropy production is subextensive with the broken detailed balance.