Perturbation Theory of the Free Energy via the Mesoscopic Combined Partition Function (opens in new tab)

We develop a systematic perturbation theory for the Helmholtz free energy of a classical $N$-body system within the mesoscopic framework of~\cite{OsanoMeso,OsanoExtensivity}. The combined coarse-graining operator $\mathcal{C}=\mathcal{C}_x\circ\mathcal{C}_p$ acting on single-particle phase space partitions it into product cells $C_{i,\alpha}=V_i\times\Pi_\alpha$ and generates a mesoscopic partition function $\mathcal{Z}_{\rm meso}(\lambda)$ whos...