  3. A crucial new ingredient in the argument is the distinction between micro- and macrostates. Note in particular that where in the previous work the distribution function \(f\) was identified with a probability (namely of a molecular state), in the present paper it, or its discrete analogy \(Z\) is a description of the macrostate of the gas. Probabilities are not assigned to the particles, but to the macrostate of the gas as a whole. According to Klein (1973, 84), this conceptual transition in 1877b marks the birth of statistical mechanics. While this view is not completely correct (as we have seen, Boltzmann 1868 already applied probability to the total gas), it is true that (1877b) is the first occasion where Boltzmann identifies probability of a gas state with relative volume in phase space, rather than its relative time of duration.