On the generalization of statistical thermodynamic functions by a Riccati differential equation.

5th International Conference on Mathematical Modeling in Physical Sciences

物理学;数学

Peña, J.J.^1 ; Rubio-Ponce, A.^1 ; Morales, J.^1

Universidad Autónoma Metropolitana - Azcapotzalco, CBI - Area de Fisica Atómica Molecular Aplicada, Av. San Pablo 180, México, D.F.

02200, Mexico^1

关键词: Internal energies;    Monatomic gas;    Nonlinear differential equation;    Particular solution;    Partition functions;    Riccati differential equation;    Thermodynamic functions;    Very low temperatures;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/738/1/012095/pdf
DOI  :  10.1088/1742-6596/738/1/012095

来源: IOP

【 摘 要 】

In this work, we propose a non-linear differential equation of Riccati-type, where the standard partition function Z(T) is taken as its particular solution leading to their generalization Zg(T); from there, other related statistical thermodynamic functions are generalized. As an useful application of our proposal, other thermodynamic functions, namely, the internal energy, heat capacity, Helmholtz free energy and entropy, associated to the model of the ideal monatomic gas in D-dimensions are generalized. According to our results, thermodynamic properties derived from the standard partition functions by means of ordinary statistical mechanics are incomplete. In fact, although asymptotically with the increasing of temperature the generalized statistical thermodynamic functions reduce to the standard ones, these contain an extra term which is dominant at very low temperature indicating that standard findings should be corrected.