Tightest bound on hidden entropy production from partially observed dynamics

Stochastic thermodynamics allows us to define heat and work for microscopic systems far from thermodynamic equilibrium, based on observations of their stochastic dynamics. However, a complete account of the energetics necessitates that all relevant nonequilibrium degrees of freedom are resolved, which is not feasible in many experimental situations. A simple approach is to map the visible dynamics onto a Markov model, which produces a lower-bound estimate of the entropy production. The bound, however, can be quite loose, especially when the visible dynamics only have small or vanishing observable currents. An alternative approach is presented that uses all observable data to find an underlying hidden Markov model responsible for generating the observed non-Markovian dynamics. For masked Markovian kinetic networks, one obtains the tightest possible lower bound on entropy production of the full dynamics that is compatible with the observable data. The formalism is illustrated with a simple example system.

Automated summary

Stochastic thermodynamics allows defining heat and work for microscopic systems far from equilibrium, although a complete account of energetics may be challenging due to unresolved nonequilibrium degrees of freedom. Mapping visible dynamics onto a Markov model can produce a lower-bound estimate of entropy production, but this bound may be loose with small observable currents. Another approach involves using all observable data to uncover a hidden Markov model responsible for generating non-Markovian dynamics, resulting in a tightest possible lower bound on entropy production for masked Markovian kinetic networks. Illustration of the formalism is demonstrated with a simple example system.