Can we formulate a resource theory of renormalization-group flow?

Statement

Problem 2.7 of Goto et al.: can RG flow be cast as a resource theory, with $c$- and $a$-type quantities (and their holographic counterparts) appearing as monotones under coarse-graining treated as a free operation?

Why It Matters

Adjacent rather than central to the group, but it touches two threads the group cares about: monotonicity of information under coarse-graining (the relative-entropy machinery) and the RG/confinement physics of the gribov-zwanziger program. A resource-theoretic $c$-theorem would be a clean “irreversibility of RG = monotone” statement.

What We Know

• $c$- (2d), $a$- (4d) theorems establish irreversibility of RG; entropic proofs (Casini–Huerta) already use relative entropy / strong subadditivity.
• Holographically, RG = radial evolution in AdS; monotonicity is geometric (null energy condition).
• A full free-operation/monotone formalization is not standard.

Possible Approaches

• Identify coarse-graining as a free operation and the $a$-function as the induced monotone.
• Relate to the entropic $c$-theorem, which is already relative-entropy-based.

Related Questions

• resource-theory-monotones-in-qft, free-states-and-operations-for-resource-theory-in-qft, holographic-resource-theory
• relative-entropy-interacting-theories