Then, the temperature is raised instantaneously to T r , so both the temperature and the volume agree with the same equilibrium state. Naively, one expects that nothing should happen when the system is at V = V e q ( T r ) and T = T r . But instead, the volume of the system first increases and then relaxes back to V e q ( T r ) , while the temperature is held constant at T r . This non-monotonic behavior in time of the volume V ( t ) after the jump in the temperature can be simply captured by: