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In macroscopic systems behavior is usually reproducible and fluctuations,which are deviations from the typically observed mean values, are small. Butalmost all inverse problems in the physical and biological sciences areill-posed and these fluctuations are highly 'amplified'. Using stochasticthermodynamics we describe a system in equilibrium kicked to a state far fromequilibrium and the following dissipative process back to equilibrium. From theobserved value at a certain time after the kick the magnitude of the kickshould be estimated, which is such an ill-posed inverse problem andfluctuations get relevant. For the model system of a kicked Brownian particlethe time-dependent probability distribution, the information loss about themagnitude of the kick described by the Kullback-Leibler divergence, and theentropy production derived from the observed mean values are given. Theequality of information loss caused by fluctuations and mean entropy productionis shown for general kicked dissipative processes from stochasticthermodynamics following the derivation of the Jarzynski and Crooks equalities.The information-theoretical interpretation of the Kullback-Leibler divergence(Chernoff-Stein Lemma) allows us to describe the influence of the fluctuationswithout knowing their distributions just from the mean value equations and thusto derive very applicable results, e.g., by giving thermodynamic limits ofspatial resolution for imaging.

Information loss and entropy production during dissipative processes in a macroscopic system kicked out of the equilibrium