  Systems driven away from thermal equilibrium constantly deliver entropy to
their environment. Determining this entropy production requires detailed
information about the system's internal states and dynamics. However, in most
practical scenarios, only a part of a complex experimental system is accessible
to an external observer. In order to address this challenge, two notions of
partial entropy production have been introduced in the literature as a way to
assign an entropy production to an observed subsystem: one due to Shiraishi and
Sagawa [Phys. Rev. E 91, 012130 (2015)] and another due to Polettini and
Esposito [arXiv:1703.05715 (2017)]. We show that although both of these schemes
provide a lower bound on the total entropy production, the latter -- which
utilizes an effective thermodynamics description-- gives a better estimate of
the total dissipation. Using this effective thermodynamic framework, we
establish a partitioning of the total entropy production into two contributions
that individually verify integral fluctuation theorems: an observable partial
entropy production and a hidden entropy production assigned to the unobserved
subsystem. Our results offer broad implications for both theoretical and
empirical systems when only partial information is available.
