  We propose a method to interpolate dynamics of von Neumann and classical
master equations with an arbitrary mixing parameter to investigate the thermal
effects in quantum dynamics. The two dynamics are mixed by intervening to
continuously modify their solutions, thus coupling them indirectly instead of
directly introducing a coupling term. This maintains the quantum system in a
pure state even after the introduction of thermal effects and obtains not only
a density matrix but also a state vector representation. Further, we
demonstrate that the dynamics of a two-level system can be rewritten as a set
of standard differential equations, resulting in quantum dynamics that includes
thermal relaxation. These equations are equivalent to the optical Bloch
equations at the weak coupling and asymptotic limits, implying that the
dynamics cause thermal effects naturally. Numerical simulations of
ferromagnetic and frustrated systems support this idea. Finally, we use this
method to study thermal effects in quantum annealing, revealing nontrivial
performance improvements for a spin glass model over a certain range of
annealing time. This result may enable us to optimize the annealing time of
real annealing machines.
