Second law of thermodynamics is ingrained within quantum mechanics

Abstract

We show that the second law of thermodynamics is rooted in quantum mechanics, inasmuch as allowing the substitution of the Boltzmann constant k and temperature with respectively the Planck constant and quantum numbers. In particular, we will see that the entropy S becomes proportional to the natural logarithm of the average of the squared quantum numbers n2‾, where each quantum number is associated with a quantum state of the constituents of the thermodynamical system under consideration. It is important to stress that the present approach furnishes the corrected Boltzmann entropy expression. Thus, instead of S=klnΩ, with Ω in the former signifying the number of Boltzmann microstates, we land at S=klnn2‾ The results obtained are discussed.