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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.

Dark breather using symmetric Morse, solvent and external potentials for DNA breathing