The κ-Generalizations of Stirling Approximation and Multinominal Coefficients

As is well-known in the fields of statistical mechanics, Ludwig Boltzmann clarified the concept of entropy. He considered that a macroscopic system consists of a large number of particles. Each particle is assumed to be in one of the energy levels, Ei (i = 1, . . . , k), and the number of particles in the energy level, Ei, is denoted by ni. The total number of particles is then n = ∑k i=1 ni, and the total energy of the macrostate is E = ∑