Partition sum in vibron model in case of non-additivity (nano-sized objects)

TL;DR

This paper develops a generalized partition sum for nano-sized objects considering non-additivity within nanothermodynamics, using vibron algebraic methods and combinatorial averaging to account for size-dependent effects.

Contribution

It introduces a novel approach to construct the partition sum for non-additive nano-objects using vibron models and combinatorial statistics, extending Hill's nanothermodynamics.

Findings

Derived expressions for energy levels of nano-objects.

Formulated a factorisable partition sum for non-additive systems.

Demonstrated the applicability to nanoparticle thermodynamics.

Abstract

We consider the problem of building an expression for the partition sum in case of non-additivity (nano-sized objects), in the framework of Hill's nanothermodynamics. Having to use not the additivity concept leads to the problem of building the generalised (Hill's) partition sum on base of the combinatorial statistics averaging. Expressions for the energy of the object are built on base of the vibron (algebraic) method, also using the author's model of size dependency of numbers of structural elements of the object. Next, the combinatorial-statistical averaging is introduced for the Hamiltonian matrix elements. The final result is represented by the expressions for the nano-sized object's individual quantum states' energies and the partition sum allowing the factorisation. Keywords: nanoparticles, nanothermodynamics, vibron model, algebraic method, Lie algebras, combinatorics, compositions