  Thermodynamics is usually formulated on the presumption that the observer has
complete information about the system he/she deals with: no parasitic current,
exact evaluation of the forces that drive the system. For example, the
acclaimed Fluctuation Relation (FR), relating the probability of time-forward
and time-reversed trajectories, assumes that the measurable transitions suffice
to characterize the process as Markovian (in our case, a continuous-time jump
process). However, most often the observer only measures a marginal current. We
show that he/she will nonetheless produce an effective description that does
not dispense with the fundamentals of thermodynamics, including the FR and the
2nd law. Our results stand on the mathematical construction of a hidden time
reversal of the dynamics, and on the physical requirement that the observed
current only accounts for a single transition in the configuration space of the
system. We employ a simple abstract example to illustrate our results and to
discuss the feasibility of generalizations.
