Recently, a novel concept for the computation of essential features of the dynamics of Hamiltonian systems (such as molecular dynamics) has been proposed. The realization of this concept had been based on subdivision techniques applied to the Frobenius-Perron operator for the dynamical system. The present paper suggests an alternative but related concept that merges the conceptual advantages of the dynamical systems approach with the appropriate statistical physics framework. This approach allows us to define the phrase "conformation" in terms of the dynamical behavior of the molecular system and to characterize the dynamical stability of conformations. In a first step, the frequency of conformational changes is characterized in statistical terms leading to the definition of some Markov operator T that describes the corresponding transition probabilities within the canonical ensemble. In a second step, a discretization of T via specific hybrid Monte Carlo techniques is shown to lead to a stochastic matrix P. With these theoretical preparaions, an identification algorithm for conformations (to be presented in a later paper) is applicable. It is demonstrated that the discretization of T can be restricted to few essential degrees of freedom so that the combinatorial explosion of discretization boxes is prevented and biomolecular systems can be attacked. Numerical results for the n-pentane molecule and the triribonucleotide adenylyl(3 -5 )cytidylyl(3 -5 )cytidin are given and interpreted.