Boltzmann’s H-theoremH-theorem (1872) was explicitlyLille University conceivedIEMN in order to proofProof Clausius’ Second LawLaw (1850s) and for cyclicCyclic processesProcess only (1854). Secondary literature used to join the function EE function, in Boltzmann’s 1872–paper, to the development of EntropyEntropy. However, Clausius’ Second Law for cyclical processes did not deal with Entropy; moreover, in a cyclic processProcess, entropy variation, being a state function, is necessarily equal to zero. Later, Clausius introduced the Entropy quantity in order to settle the framework of non-cyclic processes mathematically (1865; 1872). In this paper we will shed light on this issue through the textual analysisAnalysis of Clausius and Boltzmann’s seminal works; a critical discussion of the main historiographyHistoriography of the H-theoremH-theorem and its interplay with EntropyEntropy will be presented as well.