Probing the extensive nature of entropy

24th IUPAP Conference on Computational Physics

物理学;计算机科学

Salagaram, T.^1 ; Chetty, N.^1,2

Department of Physics, University of Pretoria, Pretoria, 0001, South Africa^1

National Institute for Theoretical Physics, 2000, Gauteng, South Africa^2

关键词: Finite size;    Microcanonical ensembles;    Non-interacting particles;    Numerical scheme;    Single particle spectrum;    Statistical entropy;    Thermodynamic limits;    Thermodynamic quantities;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/454/1/012074/pdf
DOI  :  10.1088/1742-6596/454/1/012074

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

We have devised a general numerical scheme applied to a system of independent, distinguishable, non-interacting particles, to demonstrate in a direct manner the extensive nature of statistical entropy. Working within the microcanonical ensemble, our methods enable one to directly monitor the approach to the thermodynamic limit (N) in a manner that has not been known before. We show that (sN- s) N-αwhere sNis the entropy per particle for N particles and S is the entropy per particle in the thermodynamic limit. We demonstrate universal behaviour by considering a number of different systems each defined by its unique single-particle spectrum. Various thermodynamic quantities as a function of N may be computed using our methods; in this paper, we focus on the entropy, the chemical potential and the temperature. Our results are applicable to systems of finite size, e.g. nano-particle systems. Furthermore, we demonstrate a new phenomenon, referred to as entropic interference, which manifests as a cancellation of terms in the thermodynamic limit and which results in the additive nature of entropy.