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Systems driven away from thermal equilibrium constantly deliver entropy totheir environment. Determining this entropy production requires detailedinformation about the system's internal states and dynamics. However, in mostpractical scenarios, only a part of a complex experimental system is accessibleto an external observer. In order to address this challenge, two notions ofpartial entropy production have been introduced in the literature as a way toassign an entropy production to an observed subsystem: one due to Shiraishi andSagawa [Phys. Rev. E 91, 012130 (2015)] and another due to Polettini andEsposito [arXiv:1703.05715 (2017)]. We show that although both of these schemesprovide a lower bound on the total entropy production, the latter -- whichutilizes an effective thermodynamics description-- gives a better estimate ofthe total dissipation. Using this effective thermodynamic framework, weestablish a partitioning of the total entropy production into two contributionsthat individually verify integral fluctuation theorems: an observable partialentropy production and a hidden entropy production assigned to the unobservedsubsystem. Our results offer broad implications for both theoretical andempirical systems when only partial information is available.

Hierarchical Bounds on Entropy Production Inferred from Partial Information