Utilizing time-series measurements for entropy-production estimation in partially observed systems

Estimating the dissipation, or the entropy-production rate (EPR), can provide insights into the underlying mechanisms of nonequilibrium-driven processes. However, in practical experimental settings, precise quantification of the EPR can be challenging, as only partial information is typically accessible. Here, we explore the relationship between the observed information and the accuracy of EPR estimation. We employ a range of coarse-grained time-series trajectory data, simulating scenarios where varying degrees of information are available. We discover a hierarchy of lower bounds on the total EPR, demonstrating that an increasing amount of information can be leveraged for obtaining tighter EPR estimation, underscoring the critical role of exploiting the available data. Moreover, we introduce a technique for utilizing waiting times within hidden states and tightening the lower bound on the total EPR for some cases. This approach highlights the potential of hidden features within the data to provide valuable insights into the dissipative dynamics of complex systems.