Why Thermodynamic Entropy and Statistical Entropy are Two Different Physical Quantities

Background: Historically, the coincidence of classical thermodynamic entropy and statistical entropy is based on an assumption (the so-called Boltzmann-Planck relation). The study shows that the Boltzmann-Planck relation is not valid in general. Aims: The study demonstrates that thermodynamic entropy is a physical entity distinct from statistical entropy. Methods: Initially, the entropy of ideal gases is examined and demonstrated to be independent of the gas volume. The ideal gas's true entropy is then expressed correctly. Results: The Boltzmann-Planck entropy equation is demonstrated to be incapable of describing the thermodynamic entropy of ideal gases. Conclusion: In general, the Boltzmann-Planck entropy cannot be considered a statistical interpretation of the thermodynamic entropy. The two entropies represent two different physical quantities. The physical quantity that enters the second law of thermodynamics is the thermodynamic entropy, not the statistical entropy. The study advocates for a fundamental rethinking of today's statistical understanding of thermodynamics.