  We theoretically investigate the thermally induced back-action effects in
absorption-sensitive micro- and nanomechanical resonators. We propose a unified
approach, enabling to simultaneously address both the effective dynamics and
non-equilibrium phononic state, depending on the position of a confined sensing
(and heating) probe at the surface of the mechanical device. We present an
analytical solution for a unidimensional resonator whose thermomechanical
deformation profile generally follows that of the mechanical losses. In
particular, we find that both the dynamics and the mechanical fluctuations
strongly depend on the loss distribution. The effect of the quantum
fluctuations of the heat source is also discussed. Our approach provides a
thorough, general platform for analyzing thermal back-action effects and their
consequences, which may be of significance for future development in
ultrasensitive nanomechanical research.
