Revisiting Gibbs paradox: Resolving misconceptions and addressing challenges

The Gibbs paradox explores critical aspects of entropy in gas mixing and its implications for thermodynamics. The paradox is rooted in three key elements: the independence of entropy on the identity of gases, the extensity puzzle, and the absence of entropy change when identical gases mix. This paper revisits the Gibbs paradox, beginning with a concise introduction to its core principles. It examines the problem of two ideal gases and explores the mixing behavior through macroscopic thermodynamic properties. Using Gibbs' methodology, the study analyzes the scenario of mixing two types of argon, which differ only subtly, and evaluates the entropy addition for an ideal gas mixture. The investigation extends to quantum mechanics, addressing challenges related to particle indistinguishability and the role of quantum statistical mechanics. This perspective provides a refined understanding of the paradox, bridging the gap between the macroscopic and microscopic interpretations. The study concludes by synthesizing insights from thermodynamics and quantum mechanics, highlighting their relevance in resolving the paradox. It emphasizes the significance of particle identity in entropy calculations and the consistency of statistical mechanics frameworks. Ultimately, this revisitation underscores the enduring importance of the Gibbs paradox in understanding entropy, particle distinguishability, and the interplay between classical and quantum domains.