Nonadditivity in Quantum Field Theory: Replica Energies, Scaling Filters, and the Renormalization Group (opens in new tab)

Extensive systems have a simple thermodynamic signature: the logarithm of the partition function scales homogeneously with the size of the system. We show that the failure of this scaling, measured by the replica energy ${\cal E}$, provides a useful bridge between statistical mechanics and quantum field theory. The associated differential operator $(1-\frac1d L\partial_L)$ removes the leading bulk contribution to $W=\log Z$ and isolates the pa...