A Langevin canonical framework for a chiral two--level system coupled to a bath of harmonic oscillators is developed within a coupling scheme different to the well known spin-boson model. Thermal equilibrium values are reached at asymptotic times by
solving the corresponding set of non--linear coupled equations in a Markovian regime. In particular, phase difference thermal values (or, equivalently, the so--called coherence factor) and heat capacity through energy fluctuations are obtained and discussed in terms of tunneling rates and asymmetries.
The trajectories of a qubit dynamics over the two-sphere are shown to be geodesics of certain Riemannian or physically-sound Lorentzian manifolds, both in the non-dissipative and dissipative formalisms, when using action-angle variables. Several aspe
cts of the geometry and topology of these manifolds (qubit manifolds) have been studied for some special physical cases.
