  An exactly solvable Kitaev model in a two-dimensional square lattice exhibits
a topological quantum phase transition which is different from the
symmetry-breaking transition at zero temperature. When the ground state of a
non-linearly perturbed Kitaev model with different strengths of perturbation
taken as the initial state is quenched to a pure Kitaev model, we demonstrate
that various features of the dynamical state, such as Loschmidt echo,
time-averaged multipartite entanglement, can determine whether the initial
state belongs to the topological phase or not. Moreover, the derivatives of the
quantifiers can faithfully identify the topological quantum phase transition,
present in equilibrium. When the individual qubits of the lattice interact with
the local thermal bath repeatedly, we observe that block entanglement can
nevertheless distinguish the phases from which the system starts evolution.
