Generalized-Lorentzian thermodynamics

We extend the recently developed non-gaussian thermodynamic formalism [R.A. Treumann, Physica Scripta, 59, 19 (1999)] of a (presumably strongly turbul ent) non-Markovian medium to its most general form that allows for the form ulation of a consistent thermodynamic theory. Ail thermodynamic functions, including the definition of the temperature, am shown to be meaningful. The thermodynamic potential from which all relevant physical information in eq uilibrium can be extracted, is defined consistently. The most important fin dings are the following two: (1) The temperature is defined exactly in the same way as in classical statistical mechanics as the derivative of the ene rgy with respect to the entropy at constant volume. (2) Observables am defi ned in the same way as in Boltzmannian statistics as the linear averages of the new equilibrium distribution function. This lets us conclude that the new state is a real thermodynamic equilibrium in systems capable of strong turbulence with the new distribution function replacing the Boltzmann distr ibution in such systems. We discuss the ideal gas, find the equation of sta te, and derive the specific heat and adiabatic exponent for such a gas. We also derive the new Gibbsian distribution of states. Finally we discuss the physical reasons for the development of such states and the observable pro perties of the new distribution function.