Transitive relation

Entropy, Free Energy, and the Second Law of Thermodynamics

Published in Jeffrey Olafsen, Sturge’s Statistical and Thermal Physics, 2019

Equation (5.7) shows that equality of (∂S∂U)V is a transitive relation, so that this equation is equivalent to the zero’th law of thermodynamics (see Section 2.1). It follows that (∂S∂U)V, or any monotonic single-valued function of it, defines a scale of temperature, which is absolute in the sense that the definition is independent of the properties of any particular substance.

Set Theory for Concept Modeling

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Purchase Book

Published in Richard M. Golden, Statistical Machine Learning, 2020

Richard M. Golden

A reflexive, symmetric, and transitive relation R on set S is called an equivalence relation on S. If R is an equivalence relation, then the set {y : (x, y) ∈ R} is called the equivalence class of x with respect to the equivalence relation R.

A note on the complexity of S4.2

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Journal Information

Published in Journal of Applied Non-Classical Logics, 2021

Aggeliki Chalki, Costas D. Koutras, Yorgos Zikos

A partial order is a reflexive, antisymmetric and transitive relation. A strict order is an irreflexive and transitive relation; a strict order gives rise to a corresponding partial order and vice versa (Davey & Priestley, 2002). A partial pre-order (or quasi-order) is a reflexive and transitive binary relation. Following a rather common abuse of terminology, when speaking about a frame , where is a partial pre-order (or a partial order) we will call the frame ‘a partial pre-order’ (or ‘a partial order’) instead of a ‘pre-ordered set’ (or a poset, a ‘partially ordered set’).

Transitive relation

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Entropy, Free Energy, and the Second Law of Thermodynamics

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