  Motivated by stochastic models of climate phenomena, the steady-state of a
linear stochastic model with additive Gaussian white noise is studied.
Fluctuation theorems for nonequilibrium steady-states provide a constraint on
the character of these fluctuations. The properties of the fluctuations which
are unconstrained by the fluctuation theorem are investigated and related to
the model parameters. The irreversibility of trajectory segments, which
satisfies a fluctuation theorem, is used as a measure of nonequilibrium
fluctuations. The moments of the irreversibility probability density function
(pdf) are found and the pdf is seen to be non-Gaussian. The average
irreversibility goes to zero for short and long trajectory segments and has a
maximum for some finite segment length, which defines a characteristic
timescale of the fluctuations. The initial average irreversibility growth rate
is equal to the average entropy production and is related to
noise-amplification. For systems with a separation of deterministic timescales,
modes with timescales much shorter than the trajectory timespan and whose noise
amplitudes are not asymptotically large, do not, to first order, contribute to
the irreversibility statistics, providing a potential basis for dimensional
reduction.
