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As the title says we want to answer the question; how and why doesstatistical mechanics work? As we know from the most used prescription of Gibbswe calculate the phase space averages of dynamical quantities and we find thatthese phase averages agree very well with experiments. Clearly actualexperiments are not done on a hypothetical ensemble they are done on the actualsystem in the laboratory and these experiments take a finite amount of time.Thus it is usually argued that actual measurements are time averages and theyare equal to phase averages due to ergodicity. Aim of the present review is toshow that ergodicity is not relevant for equilibrium statistical mechanics(with Tolman and Landau). We will see that the solution of the problem is inthe very peculiar nature of the macroscopic observables and with the very largenumber of the degrees of freedom involved in macroscopic systems as firstpointed out by Khinchin. Similar arguments are used by Landau based upon theapproximate property of "Statistical Independence". We review these ideas indetail and in some cases present a critique. We review the role of chaos(classical and quantum) where it is important and where it is not important. Wecriticise the ideas of E. T. Jaynes who says that the ergodic problem isconceptual one and is related to the very concept of ensemble itself which is aby-product of frequency theory of probability, and the ergodic problem becomesirrelevant when the probabilities of various micro-states are interpreted withLaplace-Bernoulli theory of Probability (Bayesian viewpoint). In the end wecritically review various quantum approaches (quantum-statistical typicalityapproaches) to the foundations of statistical mechanics.

How and why does statistical mechanics work