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A central concept in the connection between physics and information theory isentropy, which represents the amount of information extracted from the systemby the observer performing measurements in an experiment. Indeed, Jaynes'principle of maximum entropy allows to establish the connection between entropyin statistical mechanics and information entropy. In this sense, the dissipatedenergy in a classical Hamiltonian process, known as the thermodynamic entropyproduction, is connected to the relative entropy between the forward andbackward probability densities. Recently, it was revealed that energeticinefficiency and model inefficiency, defined as the difference in mutualinformation that the system state shares with the future and past environmentalvariables, are equivalent concepts in Markovian processes. As a consequence,the question about a possible connection between model unpredictability andenergetic inefficiency in the framework of classical physics emerges. Here, weaddress this question by connecting the concepts of random behavior of aclassical Hamiltonian system, the Kolmogorov-Sinai entropy, with its energeticinefficiency, the dissipated work. This approach allows us to providemeaningful interpretations of information concepts in terms of thermodynamicquantities.

Kolmogorov-Sinai entropy and dissipation in driven classical Hamiltonian systems