  A central result that arose in applying information theory to the stochastic
thermodynamics of nonlinear dynamical systems is the Information-Processing
Second Law (IPSL): the physical entropy of the universe can decrease if
compensated by the Shannon-Kolmogorov-Sinai entropy change of appropriate
information-carrying degrees of freedom. In particular, the asymptotic-rate
IPSL precisely delineates the thermodynamic functioning of autonomous
Maxwellian demons and information engines. How do these systems begin to
function as engines, Landauer erasers, and error correctors? Here, we identify
a minimal, inescapable transient dissipation engendered by physical information
processing not captured by asymptotic rates, but critical to adaptive
thermodynamic processes such as found in biological systems. A component of
transient dissipation, we also identify an implementation-dependent cost that
varies from one physical substrate to another for the same information
processing task. Applying these results to producing structured patterns from a
structureless information reservoir, we show that "retrodictive" generators
achieve the minimal costs. The results establish the thermodynamic toll imposed
by a physical system's structure as it comes to optimally transduce
information.
