  We prove the equivalence among symmetricity, time reversibility, and zero
entropy production of the stationary solutions of linear stochastic
differential 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
reversibility, we show that there is a contradistinction between any
1-dimensional stationary Gaussian process and stationary Gaussian process of
dimension $n>1$. A concrete criterion for differentiating stationarity and
sweeping behavior is also obtained. The mathematical result is a natural
generalization of Einstein's fluctuation-dissipation relation, and provides a
rigorous basis for the isothermal irreversibility in a linear regime which is
the basis for applying Onsager's theory to macromolecules in aqueous solution.
