We prove the equivalence among symmetricity, time reversibility and zero en
tropy production of the stationary solutions of linear stochastic different
ial equations. A sufficient and necessary reversibility condition expressed
in terms of the coefficients of the equations is given. The existence of a
linear stationary irreversible process is established. Concerning reversib
ility, we show that there is a contradistinction between any one-dimensiona
l stationary Gaussian process and a stationary Gaussian process of dimensio
n n > 1. A concrete criterion for differentiating stationarity and sweeping
behaviour is also obtained. The mathematical result is a natural generaliz
ation of Einstein's fluctuation-dissipation relation, and provides a rigoro
us basis for the isothermal irreversibility in a linear regime, which is th
e basis for applying Onsager's theory to macromolecules in aqueous solution
.