Making thermodynamic functions of nanosystems intensive

TL;DR

This paper investigates the limitations of existing scaling methods to make thermodynamic functions of nanosystems intensive and proposes a generalized parameter based on potential energy per particle to achieve this goal.

Contribution

It provides a theoretical justification for a generalized scaling parameter that can make thermodynamic functions of nanosystems intensive, extending previous approaches.

Findings

Existing scaling parameters fail for nanosystems.

A new generalized parameter is proportional to potential energy per particle.

The proposed parameter successfully makes thermodynamic functions intensive.

Abstract

The interaction potential energy among particles in many systems is of the form of r^-(alpha), at least at long distances. It has been argued that, in systems for which (alpha) < d (d is the space dimension) we encounter with nonextensive (nonintensive) thermodynamic functions. A scaling parameter N~ has been introduced to make nonextensive (nonintensive) thermodynamic functions of such systems extensive (intensive) functions. Our simulation results show that this parameter is not capable of making thermodynamic functions of a nanosystem extensive (intensive). Here we have presented a theoretical justification for the ability of such scaling parameter, and then we have generalized this scaling parameter to be capable of making nonextensive (nonintensive) thermodynamic functions of nanosystems extensive (intensive). This parameter is proportional to the potential energy per particle at zero temperature.