Physical meaning of nonextensive term in Massieu functions

In this paper we explore the significance of nonextensive terms in Massieu functions. Finite-size effects are in many cases dominated by a term proportional to the surface area. Nevertheless, in numerical simulations of finite systems with periodic boundary conditions, the nonextensive term can become the dominant correction to Massieu functions. This paper presents a general approach linking these nonextensive terms to thermodynamic fluctuations, demonstrating that equations of state inherently encode this information. Numerical simulations corroborate our results. The examples used are hard sphere and hard disk fluids and a one-dimensional spin lattice, emphasizing the applicability of the results across different classes of systems.