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We generalize Shannon's information theory in a nonadditive way by focusing on the source coding theorem. The nonadditive information content we adopted is consistent with the concept of the form invariance structure of the nonextensive entropy. Some general properties of the nonadditive information entropy are studied, in addition, the relation between the nonadditivity q and the codeword length is pointed out.

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Based on a generalized form of the second law of thermodynamics, in which the temperature-dependent energy levels of a system are appropriately included in entropy generation, we show that the effect reasonably appears in efficiencies of thermodynamic processes.

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A general procedure of statistical inference based on information theory AIP Conf.Singularities in the complex temperature plane at the first order phase transitions and critical points AIP Conf.The properties of a statistical complexity measure that are characterized by nonextensivity in entropy have been investigated, which is of so-called disequilibrium type. Considering the composition law for two systems with different nonextensivities ͑quasi-multiplicativity͒, a nontrivial relation between the nonextensive parameters and the fluctuating bit number in information theory has been mentioned. To see the time evolution of the nonextensive complexity measure, we examine systems having a lognormal distribution, the underlying dynamics for which is known to obey a random multiplicative process in the presence of a boundary constraint.

The performances of solar cells and thermoelectric materials are governed by thermodynamics. The material properties of these have temperature dependence due to thermal expansions of lattices and an effect of electron-phonon coupling etc. The temperature-dependent energy levels has been included in statistical mechanics, naturally requiring a rectification of the second law of thermodynamics with an effective heat. In such a framework, we show that exergy associated with internal energy of isolated systems can be increased in irreversible processes. We furthermore see how the effect of the temperature-dependent energy levels appears in the thermodynamic performance in terms of the second law efficiency.