Thermodynamics of interacting system of DNAs.

We define a DNA as a sequence of $1, 2$'s and embed it on a path of Cayley tree in such a way that each vertex of the Cayley tree belongs only to one of DNA and each DNA has its own countably many set of neighboring DNAs. The Hamiltonian of this set of DNAs is a model with two spin values considered as DNA base pairs. We describe translation invariant Gibbs measures (TIGM) of the model on the Cayley tree of order two and use them to study thermodynamic properties of the model of DNAs. We show that there is a critical temperature $T_{\rm c}$ such that (i) if temperature $T\geq T_{\rm c}$ then there exists unique TIGM; (ii) if $T

Keywords:

• DNA
• Quantum mechanics
• Hamiltonian (quantum mechanics)
• Invariant (mathematics)
• Base pair
• Mathematics
• Critical point (thermodynamics)
• Spin-½
• Vertex (geometry)
• A-DNA
• Mathematical physics

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