  Complementary strands in DNA double helix show temporary fluctuational
openings which are essential to biological functions such as transcription and
replication of the genetic information. Such large amplitude fluctuations,
known as the breathing of DNA, are generally localized and, microscopically,
are due to the breaking of the hydrogen bonds linking the base pairs
(\emph{bps}). I apply imaginary time path integral techniques to a mesoscopic
Hamiltonian which accounts for the helicoidal geometry of a short circular DNA
molecule. The \emph{bps} displacements with respect to the ground state are
interpreted as time dependent paths whose amplitudes are consistent with the
model potential for the hydrogen bonds. The portion of the paths configuration
space contributing to the partition function is determined by selecting the
ensemble of paths which fulfill the second law of thermodynamics. Computations
of the thermodynamics in the denaturation range show the energetic advantage
for the equilibrium helicoidal geometry peculiar of B-DNA. I discuss the
interplay between twisting of the double helix and anharmonic stacking along
the molecule backbone suggesting an interesting relation between intrinsic
nonlinear character of the microscopic interactions and molecular topology.
