  We use an alternative approach to study the quantum phase transition in a
coupled cavity lattice at finite temperature. As an illustrative example, we
investigate the behaviors of the trace distance and quantum phase transition in
a Jaynes-Cummings lattice at finite temperature. It is found that the trace
distance can be used to describe the critical point of the quantum phase
transition at finite low temperatures and the critical points are sensitive to
the atom-field interaction strength and the detuning factor. For
non-equilibrium states, we demonstrate that the time evolution of the trace
distance's maximum value is also a good indicator of the critical points.
Moreover, we show that the scaling behavior of derivative of the trace distance
at the critical points and the scaling rule are dependent on the external
parameters of the Hamiltonian.
