Active matter has attracted recent attentions.However,explicit physical quantifications and characterizations are still challenging.In this work,we explore how the input chemical energy pump can create a new active phase,the limit cycle phase,induce phase transitions between mono-stable and limit cycle for the active matter,and change the corresponding underlying landscape topography.Such non-equilibrium phase and non-equilibrium phase transitions cannot exist in the isolated Hamiltonian systems without energy input from the environments.We illustrate how energy pump can give rise to the non-zero flux breaking the detailed balance.Furthermore,we show how this leads to the dissipation in terms of the entropy production rate which is correlated strongly with the flux.Finally,we found that it is the flux induced by the energy pump that leads to the time reversal symmetry breaking.In fact,the degree of the time reversal symmetry breaking can be used to infer the flux or the underlying energy pump for driving the active matter.