Thermodynamic adiabatic processes have no entropy change. Typically, an external control modifies the state. A quantum version of an adiabatic process can be modeled by an externally controlled time dependent Hamiltonian H ( t ) . If the system is isolated, the dynamics are unitary, and therefore, S v n is a constant. A quantum adiabatic process is defined by the energy entropy S E being constant. The quantum adiabatic condition is therefore equivalent to no net change in the population of the instantaneous energy levels. This implies that the Hamiltonian should commute with itself at different times: [ H ( t ) , H ( t ′ ) ] = 0 .