Casimir versus Helmholtz forces in the Gaussian model: exact results for Dirichlet--Dirichlet, Neumann--Dirichlet, Neumann--Neumann, and periodic boundary conditions

Daniel Dantchev, Joseph Rudnick

We present results and compare the behavior of two fluctuation-induced forces pertinent for their corresponding ensembles: the critical Casimir force in the grand canonical (fixed…