The definitions of the temperature in the nonextensive statistical thermodynamics based on Tsallis entropy are analyzed. A definition of pressure is proposed for nonadditive systems by using a nonadditive effective volume. The thermodynamics of nonadditive photon gas is discussed on this basis. We show that the Stefan-Boltzmann law can be preserved within nonextensive thermodynamics. PACS : 05.20.-y, 05.70.-a, 02.50.-r 1 Tsallis entropy is given by S = i p q i −1 1−q , (q ∈ R)[1]

The problem of factorization of a nonextensive probability distribution is discussed. It is shown that the correlation energy between the correlated subsystems in the canonical composite system can not be neglected even in the thermodynamic limit. In consequence, the factorization approximation should be employed carefully according to different systems. It is also shown that the zeroth law of thermodynamics can be established within the framework of the Incomplete Statistical Mechanics (ISM ).

We show that Abe's general pseudoadditivity for entropy prescribed by thermal equilibrium in nonextensive systems holds not only for entropy, but also for energy. The application of this general pseudoadditivity to Tsallis entropy tells us that the factorization of the probability of a composite system into product of the probabilities of the subsystems is just a consequence of the existence of thermal equilibrium and not due to the independence of the subsystems. 05.20.-y,05.70.-a,05.90.+m 1

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This is a study of the information evolution of complex systems by a geometrical consideration. We look at chaotic systems evolving in fractal phase space. The entropy change in time due to the fractal geometry is assimilated to the information growth through the scale refinement. Due to the incompleteness of the state number counting at any scale on fractal support, the incomplete normalization i p q i = 1 is applied throughout the paper, where q is the fractal dimension divided by the dimension of the smooth Euclidean space in which the fractal structure of the phase space is embedded. It is shown that the information growth is nonadditive and is proportional to the traceform i p i − i p q i which can be connected to several nonadditive entropies. This information growth can be extremized to give power law distributions for these non-equilibrium systems. It can also lead to a nonextensive thermodynamics for heterogeneous systems which contain subsystems each having its own q. It is shown that, within this thermodynamics, the Stefan-Boltzmann law of blackbody radiation can be preserved.