  We consider stochastic thermodynamics as a theory of statistical inference
for experimentally observed fluctuating time-series. To that end, we introduce
a general framework for quantifying the knowledge about the dynamical state of
the system on two scales: a fine-grained or microscopic, deterministic and a
coarse-grained or mesoscopic, stochastic level of description. For a generic
model dynamics, we show how the mathematical expressions for fluctuating
entropy changes used in Markovian stochastic thermodynamics emerge naturally.
Our ideas are conceptional approaches towards (i) connecting entropy production
and its fluctuation relations in deterministic and stochastic systems and (ii)
providing a complementary information-theoretic picture to notions of entropy
and entropy production in stochastic thermodynamics.
