  Based on the tensor network state representation, we develop a nonlinear
dynamic theory coined as network contractor dynamics (NCD) to explore the
thermodynamic properties of two-dimensional quantum lattice models. By invoking
the rank-$1$ decomposition in the multi-linear algebra, the NCD scheme makes
the contraction of the tensor network of the partition function be realized
through a contraction of a local tensor cluster with vectors on its boundary.
An imaginary-time-sweep algorithm for implementation of the NCD method is
proposed for practical numerical simulations. We benchmark the NCD scheme on
the square Ising model, which shows a great accuracy. Besides, the results on
the spin-1/2 Heisenberg antiferromagnet on honeycomb lattice are disclosed in
good agreement with the quantum Monte Carlo calculations. The
quasi-entanglement entropy $S$, Lyapunov exponent $I^{lya}$ and loop character
$I^{loop}$ are introduced within the dynamic scheme, which are found to display
the ``nonlocality" near the critical point, and can be applied to determine the
thermodynamic phase transitions of both classical and quantum systems.
