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Stochastic thermodynamics allows us to define heat and work for microscopicsystems far from thermodynamic equilibrium, based on observations of theirstochastic dynamics. However, a complete account of the energetics necessitatesthat all relevant nonequilibrium degrees of freedom are resolved, which is notfeasible in many experimental situations. A simple approach is to map thevisible dynamics onto a Markov model, which produces a lower-bound estimate ofthe entropy production. The bound, however, can be quite loose, especially whenthe visible dynamics only have small or vanishing observable currents. Analternative approach is presented that uses all observable data to find anunderlying hidden Markov model responsible for generating the observednon-Markovian dynamics. For masked Markovian kinetic networks, one obtains thetightest possible lower bound on entropy production of the full dynamics thatis compatible with the observable data. The formalism is illustrated with asimple example system.

Tightest bound on hidden entropy production from partially observed dynamics