We investigate the nonequilibrium thermodynamics of a quenched XY spin chain with multi-spin interaction in a transverse field.The analytical expressions of both the average work and the relative entropy are obtained under different quenching parameters.The influences of the system parameters on the nonequilibrium thermodynamics are investigated.We find that at finite temperature the critical phenomenon induced by the multi-spin interaction and the external field can be revealed by the properties of the system nonequilibrium thermodynamics.In addition,our results indicate that the average work and the relative entropy can be used to detect both the existence and strength of the multi-spin interaction in the nonequlibrium system.