Based on the group entropy theory, in this work, we generalize the algebra of real numbers (referred to as G-algebra) along with its associated calculus, thus obtaining the algebraic structures corresponding to the Tsallis and the \(\kappa \)-statistics. From a G-deformed translation operator, we obtain its associated Schrödinger equation, that corresponds to a particle with an effective position-dependent mass determined by the G-algebra. The q-deformed (standard) Schrödinger equation results in a special case for the Tsallis (Boltzmann–Gibbs) group class. We illustrate the results with the one-dimensional potential well for the \(\kappa \) and the Tsallis classes and we obtain a family of potentials associated with the group entropy classes by first principles.

基于群熵理论，在这项工作中，我们将实数的代数（称为G-代数）及其相关的演算进行了推广，从而获得了与Tsallis和\（\ kappa \）相对应的代数结构-统计数据。从G变形的平移算符中，我们获得其关联的Schrödinger方程，该方程与具有由G代数确定的有效位置相关质量的粒子相对应。的q -deformed在用于Tsallis（玻尔兹曼-吉布斯）基团类的特殊情况（标准）薛定谔方程的结果。我们用\（\ kappa \）的一维势阱很好地说明了结果 以及Tsallis类，我们通过第一原理获得了与群熵类相关的一族电位。