Information geometry of the thermodynamic manifold

摘要

We consider the a-geometric structure of the thermodynamic man-ifold S which characterizes a given physical system. We obtain the a-Gaussian cur-vature which is the generalization of the Riemannian Gaussian curvature. We set upa submanifold Al which is a 1-flat subrnanifold of S. By introducing the Kullback-Leibler divergence, we get the optimal estimation point on M from a point on S bymeans of projection, and the optimal estimation point is unique. At last, we givean example to illustrate our results.