The Concept of Entropy in Statistical Mechanics and Stochastic Music Theory: On the Possibility of a Formal and Philosophical Isomorphism Ivano Zanzarella ivano.zanzarella@rub.de Term Paper March, 2021 Abstract Originally appeared in the field of thermodynamics, the concept of entropy, especially in its statistical acceptation, has found applications in many different disciplines, both inside and outside science. In this work we focus on the possibility of drawing an isomorphism between the entropy of Boltzmann’s statistical mechanics and that of Xenakis’s stochastic music theory. We expose the major technical aspects of the two entropies and then consider affinities and differences between them, both at syntactic and at semantic level, hereto particularly referring to the philosophical problem of the asymmetry of time. Contents 1 Introduction 1 2 Entropy in Science and Music 2 2.1 A Brief Historical and Contextual Introduction to the Concept of Entropy . 2 2.2 Entropy in Boltzmann’s Statistical Mechanics ................. 6 2.3 Entropy in Xenakis’ Stochastic Music Theory ................. 16 3 Epistemological Analysis of a Possible Isomorphism 31 3.1 Formal Affinities and Differences ........................ 31 3.2 Philosophical Affinities and Differences: The Problem of Asymmetry of Time 40 4 Conclusion 48 5 References 51 1