  We provide the full theory of thermodynamic formalism for a very general
collection of entire functions in class $\mathcal B$. This class overlaps with
the collection of all entire functions for which thermodynamic formalism has
been so far established and contains many new functions.
  The key point is that we introduce an integral means spectrum for logarithmic
tracts which takes care of the fractal behavior of the boundary of the tract
near infinity. It turns out that this spectrum behaves well as soon as the
tracts have some sufficiently nice geometry which, for example, is the case for
quasicircle, John or H\"older tracts. In this case we get a good control of the
corresponding transfer operators, leading to full thermodynamic formalism along
with its applications such as exponential decay of correlations, central limit
theorem and a Bowen's formula for the Hausdorff dimension of radial Julia sets.
  Our approach applies in particular to every hyperbolic function from any
Eremenko-Lyubich analytic family of Speiser class $\mathcal S$ provided this
family contains at least one function with H\"older tracts. The latter is, for
example, the case if the family contains a Poincar\'e linearizer.
