Paper Title
Thermodynamic Potentials Generalized from a 𝜆-Deformed Exponential Function

Abstract
Abstract - In the transformation of the effective Hamiltonian for the case of a spatially dependent mass, into its canonical form, a generalized (𝜆-deformed) Hermitian linear momentum operator p_λis deduced. Added to this, a spatial canonical transformation x_λto solve the resulting differential equation leads to a 𝜆-deformed quantum mechanics.In this scenario it is possible to propose a 𝜆-deformed exponential function 〖exp〗_λ (x)=exp⁡(x_λ) and its corresponding𝜆-deformed logarithmic partner〖ln〗_λ (x).From these results, and the definition of the internal energy U=-k ∂/∂β ln(Z), it is straightforward to get the generalized internal energyU_λ=-k ∂/∂β 〖ln〗_λ (Z_λ ) which enables a natural generalization of others thermodynamic functions such as the EntropyS_λ, the Helmholtz free energy F_λ and the heat capacity C_λ.Some particular mass distributionsm(λ;x) are used as example to illustrate the proposal. Besides, in the case of m(λ;x)=m_0 〖(1+λx)〗^(-2) our proposal leads straightforwardly to the Tsallis results obtained by solving a variational problem with suitable Lagrange parameters. Keywords - Schrödinger Equation, Position-dependent Mass, Generalized Exponential Function, Internal Energy, Thermodynamic Functions.