On the laws of thermodynamics from the escort average and on the uniqueness of statistical factors

Abstract We consider the relation between the statistical weight and the laws of thermodynamics. Our path bases on the infinitesimal perturbation from outside of the thermodynamical system. It is fair to say that the form of the first laws of thermodynamics and the Clausius' definition of thermodynamic entropy are commensurately altered once we employ the escort average of statistical weight but preserves the forms in the limit of the usual weight. We also see an example for the unique determination of the statistical factor (so-called the Gibbs theorem) in addition to the Boltzmann and the Tsallis ones.

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