  The paper is devoted to the analysis of relationships between principal
objects of the spectral theory of dynamical systems (transfer and weighted
shift operators) and basic characteristics of information theory and
thermodynamic formalism (entropy and topological pressure). We present explicit
formulae linking these objects with $t$-entropy and spectral potential.
Herewith we uncover the role of inverse rami-rate, forward entropy along with
essential set and the property of non-contractibility of a dynamical system.
