The irreversibility of RG flows on conformal defects has been a subject of great interest recently. In this talk I will present an entropy function defined on 2D spherical defects, interpolating between the defect anomaly coefficient at the fixed points. We reproduce the IR sum-rule proving irreversibility and show that the function is perturbatively monotonically decreasing. We consider an interesting physically relevant example using self-adjoint extension, providing important information beyond the epsilon expansion.