  The averaged steady-state surprisal links a driven stochastic system's
information processing to its nonequilibrium thermodynamic response. By
explicitly accounting for the effects of nonequilibrium steady states, a
decomposition of the surprisal results in an information processing First Law
that extends and tightens -- to strict equalities -- various information
processing Second Laws. Applying stochastic thermodynamics' integral
fluctuation theorems then shows that the decomposition reduces to the second
laws under appropriate limits. In unifying them, the First Law paves the way to
identifying the mechanisms by which nonequilibrium steady-state systems extract
work from information-bearing degrees of freedom. To illustrate, we analyze an
autonomous Maxwellian information ratchet that tunably violates detailed
balance in its effective dynamics. This demonstrates how the presence of
nonequilibrium steady states qualitatively alters an information engine's
allowed functionality.
