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Title: A Classic in Statistical Physics
Review: The book contains too much on the topic of irreversibility from the Boltzmann standpoint to be of much interest today, excepting one chapter: the one by Kac on functional integration and partial differential equations. Here, Kac makes Feynman's connection rigorous for the case of a Wiener process (Brownian motion) and presents the 'Feynman-Kac formula' that so many financial math texts now rave about without pushing the boundaries further mathematically to do something useful for empirical modelling in option pricing. For more in this direction, see Durrett's "Brownian Motion and Martingales in Analysis" and the final chapter in Steele's "Financial Calculus". See also papers by me now in preparation.
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