  We present a novel approach to establishing the variational principle for
Gibbs and generalized (weak and almost) Gibbs states. Limitations of a
thermodynamical formalism for generalized Gibbs states will be discussed. A new
class of intuitively weak Gibbs measures is introduced, and a typical example
is studied. Finally, we present a new example of a non-Gibbsian measure arising
from an industrial application.
