There exist extensive literature on the statistical mechanics of DNA, RNA and proteins, so extensive literature search is a must here (there is a lot in Physical Reviews, but there is even more in biology-minded publications [NCBI/PMC][1] is your friend here). I would not be surprized, if your problem has been studied and described as well, although it is a bit more exotic (just a bit, after all, RNA aligns to DNA during the transcription process, which is commonplace). I will give only a few directions for search centered on my experience with RNA structures. (Btw, note that RNA has U-s instead of T-s, which may make some difference when studying RNA-DNA coupling). The classical RNA folding approaches based on base pairing are grounded in the **Nussinov's algorithm**, although there have been many refinements (see, e.g., [here][2], [here][3] and [here][4]). The most crucial refinement is that no serious algorithm actually calculates the energy of an RNA or DNA on the basis of base pairing, but rather [as a **stacking energy** between pairs][5]. The use of dynamical programming algorithm is necessitated by the fact that one has to deal with a huge number of possible structures and calculation the partition function directly is simply not feasible. Another good place to look is bioinformatics textbooks, [Durbin and others][6] is a classic, and includes an introduction on modeling RNA structures using **context-free grammars**, a subject that has received more attention very recently. Among more exotic approaches are inferring RNA structure on the basis of correlations in a sequence alignment (I'll try to find the reference), as well as the approach based on field-theoretical large-N expansion by [Henri Orland and collaborators][7] (yes, the author of Negele&Orland's book on quantum statistical physics). Orland also has articles about protein folding, but it is a domain of its own, by far more advanced. To get closer to DNA helix, **[helix-coil transition][8]** is the basic model here, but the literature is somewhat scarce and rather dated. [1]: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6009650/ [2]: https://www.springer.com/gp/book/9781493964314 [3]: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4086783/ [4]: https://rna.urmc.rochester.edu/NNDB/turner04/index.html [5]: https://en.wikipedia.org/wiki/Nucleic_acid_thermodynamics#Nearest-neighbor_method [6]: https://www.amazon.fr/Biological-Sequence-Analysis-Probabilistic-Proteins/dp/0521629713 [7]: http://web.mit.edu/18.325/www/rmt_rna.pdf [8]: https://en.wikipedia.org/wiki/Helix%E2%80%93coil_transition_model