  The ultimate sensitivities achieved in force or mass sensing are limited by
the employed nanomechanical probes thermal noise. Its proper understanding is
critical for ultimate operation and any deviation from the underlying
fluctuation dissipation theorem should be carefully inspected. Here we
investigate an ultrasensitive vectorial force-field sensor, a singly clamped
nanowire oscillating along two quasi frequency degenerated transverse
directions. Immersing the nanowire in a non-conservative optical force field
causes dramatic modifications of its thermal noise and driven dynamics. In
regions of strong vorticity, eigenmodes orientations are distorted and lose
their initial orthogonality. Thermal noise spectra strongly deviate from the
normal mode expansion and presents an anomalous excess of noise violating the
fluctuation dissipation theorem. Our model quantitatively accounts for all
observations and underlines the role of non-axial response when patching the
fluctuation dissipation relation. These results reveal the intriguing
properties of thermal fluctuations in multimode nano-optomechanical systems and
the subtleties appearing when performing thermal noise thermometry in such
systems. They are also valid in any non-symmetrically coupled dual systems.
