  When a physical system evolves in a thermal bath at a constant temperature,
it arrives eventually to an equilibrium state whose properties are independent
of the kinetic parameters and of the precise evolution scenario. This is
generically not the case for a system driven out of equilibrium which, on the
contrary, reaches a steady-state with properties that depend on the full
details of the dynamics such as the driving noise and the energy dissipation.
How the steady state depends on such parameters is in general a non-trivial
question. Here, we approach this broad problem using a minimal model of a
two-dimensional nano-machine, the Brownian gyrator, that consists of a trapped
particle driven by fractional Gaussian noises -- a family of noises with
long-ranged correlations in time and characterized by an anomalous diffusion
exponent $\alpha$. When the noise is different in the different spatial
directions, our fractional Brownian gyrator persistently rotates. Even if the
noise is non-trivial, with long-ranged time correlations, thanks to its
Gaussian nature we are able to characterize analytically the resulting
nonequilibrium steady state by computing the probability density function, the
probability current, its curl and the angular velocity and complement our study
by numerical results.
