  A canonical framework for chiral two--level systems coupled to a bath of
harmonic oscillators is developed to extract, from a stochastic dynamics, the
thermodynamic equilibrium values of both the population difference and
coherences. The incoherent and coherent tunneling regimes are analyzed for an
Ohmic environment in terms of a critical temperature defined by the maximum of
the heat capacity. The corresponding numerical results issued from solving a
non-linear coupled system are fitted to approximate path--integral analytical
expressions beyond the so-called non-interacting blip approximation in order to
determine the different time scales governing both regimes.
