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This first volume in a two-part series presents a comprehensive study of stochastic models for many-body systems in thermal equilibrium. The authors introduce the theory of stochastic processes, and provide a detailed analysis of the properties of the canonical ensemble and its variants. This book is an essential resource for researchers and students in statistical mechanics and related fields. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
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