  We study two-dimensional spherical defects in d-dimensional Conformal Field
Theories. We argue that the Renormalization Group (RG) flows on such defects
admit the existence of a decreasing entropy function. At the fixed points of
the flow, the entropy function equals the anomaly coefficient which multiplies
the Euler density in the defect's Weyl anomaly. Our construction demonstrates
an alternative derivation of the irreversibility of RG flows on two-dimensional
defects. Moreover in the case of perturbative RG flows, the entropy function
decreases monotonically and plays the role of a C-function. We provide a simple
example to explicitly work out the RG flow details in the proposed
construction.
