Size-effect at finite temperature in a quark–antiquark effective model in phase space

A quark-antiquark effective model is studied in a toroidal topology at finite temperature. The described by Schr\"odinger equation with linear potential which embedded torus. following aspects are analysed: (i) the nonclassicality structure using Wigner function formalism; (ii) temperature and size-effects generalization of Thermofield Dynamics written phase space; (iii) order to include spin quark, Pauli-like used; (iv) analysis size-effect considered observe fluctuation ground state. size effect goes zero zero, high temperatures. results emphasize that central aspect for this model.