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In this chapter we introduce a sequence of logical statements for the adiabatic properties of systems. In particular statements which encompass different versions of Carathéodory’s Principle. The forward sector of a state \({\pmb {X}}\) is the set of states adiabatically accessible from \({\pmb {X}}\) . The geometric structure of such sectors for simple systems is determined by a set of Simple-System Axioms S–I to S–III. We show that a consequence of these axioms is the division of simple systems into two types, positive-simple and negative-simple, divided according to whether internal energy increases or decreases in an adiabatic process. The relation of the Simple-System Axioms to Carathéodory’s Principle is discussed.

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Carathéodory’s Principle and the Second Law: Adiabatic Comparability and Irrecoverability

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  • 发表日期：

    2025年

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  • David A. Lavis,
  • Roman Frigg

摘要

In this chapter we introduce a sequence of logical statements for the adiabatic properties of systems. In particular statements which encompass different versions of Carathéodory’s Principle. The forward sector of a state \({\pmb {X}}\) is the set of states adiabatically accessible from \({\pmb {X}}\) . The geometric structure of such sectors for simple systems is determined by a set of Simple-System Axioms S–I to S–III. We show that a consequence of these axioms is the division of simple systems into two types, positive-simple and negative-simple, divided according to whether internal energy increases or decreases in an adiabatic process. The relation of the Simple-System Axioms to Carathéodory’s Principle is discussed.