Entropy in Statistical Mechanics: Back to Boltzmann

Statistical entropy introduced in Boltzmann's combinatorial argument played a crucial role in the development of modern physics, yet it is limited to ideal monatomic gases. Statistical mechanics developed by Gibbs is suitable for any system, and this approach yielded important practical results. Unfortunately, the Gibbs statistical entropy remains constant during an irreversible process in the isolated system. This led to the conclusion that entropy is subjective — that entropy of a system is related to ignorance or information gained by an external observer during measurement. At present, arguments for the objectivity of entropy are related to the microcanonical Boltzmann entropy in the system phase space. The advantages and disadvantages of the Boltzmann entropy are discussed. Carnap's principle of physical magnitudes is also considered.