Abstract
The balance equation of the information entropy of a dynamical system subjected to noise is derived. Entropy flow and entropy production terms are identified, featuring such quantities as the sum of the Lyapunov exponents and the noise strength. A comparison with irreversible thermodynamics is carried out, showing that the (information) entropy production is related to the excess entropy production around a reference state averaged over the probability density, rather than to the full thermodynamic entropy production.
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