A b s t r a c t . We investigate certain dissipative dynamical systems from the aspect of the accessibility of states. Here the set of the n-dimensional probability vectors serves as state space, while i t is assumed that the dynamics can be modelled by generalized doubly stochastic matrices. We clarify what on these assumptions the set of states looks like starting from which a given state is accessible.

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We investigate the problem of distributing a given amount of heat among three systems under the following conditions: The systems are able to exhibit negative Kelvin temperatures, and heat equalization always fulfills a harmonic mixing rule+ T (2) ). Just this happens for spin systems in the high temperature approximation.

The Wigner-Kirkwood series expansion of equilibrium quantum statistics in the phase space formalism is generalized to include relativistic systems. For partition functions and all thermodynamic functions the series yields quantum corrections in terms of powers of h2 including systematic relativistic corrections given by modified Hankel functions 9@nc2/kT). An application to the symmetric relativistic quantum Toda oscillator is sketched.

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