We demonstrate an efficient formula to compute the entropy rate H(μ) of a hidden Markov process with q output symbols where at least one symbol is unambiguously received. Using an approximation to H(μ) to the first N terms we give a O(Nq) algorithm to compute the entropy rate of the hidden Markov model. We use the algorithm to estimate the entropy rate when the parameters of the hidden Markov m...

The entropy production rate (EPR) offers a quantitative measure of time reversal symmetry breaking in non-equilibrium systems. It can be defined either at particle level or the coarse-grained fields such as density; EPR for latter quantifies extent to which these behave irreversibly. In this work, we first develop general method compute scalar Langevin field theories with additive noise. This l...