| Summary: | We analyze the dynamics and the quantum thermodynamics of DNA in Symmetric-Peyrard-Bishop-Dauxois model (S-PBD) with solvent and external potentials and describe the transient conformational fluctuations using dark breather and the ground state wave function of the associate Schrodinger differential equation. We used the S-PBD, the Floquet theory, quantum thermodynamic and finite difference methods. We show that for lower coupling dark breather is present. We estimate the fluctuations or breathing of DNA. For the S-PBD model we have the stability of dark breather for k<0.004 and mobile breathers with coupling k=0.004. The fluctuations of the dark breather in the S-PBD model is approximately zero with the quantum thermodynamics. The viscous and external potential effect is direct proportional to hydrogen bond stretching.
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