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The fundamentals of thermodynamics

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	The fundamentals of thermodynamics/ by David A. Lavis, Roman Frigg.
作者:	Lavis, D. A.
其他作者:	Frigg, Roman.
出版者:	Cham :Springer Nature Switzerland : : 2025.,
面頁冊數:	xv, 499 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Theoretical, Mathematical and Computational Physics. -
電子資源:	https://doi.org/10.1007/978-3-031-77948-0
ISBN:	9783031779480

The fundamentals of thermodynamics
Lavis, D. A.

The fundamentals of thermodynamics[electronic resource] /by David A. Lavis, Roman Frigg. - Cham :Springer Nature Switzerland :2025. - xv, 499 p. :ill., digital ;24 cm. - Fundamental theories of physics,v. 2212365-6425 ;. - Fundamental theories of physics ;v.172..

Introduction -- States and Processes -- Adiabatic Processes and the First Law -- Carathéodory's Principle and the Second Law -- Thermal Equilibrium and the Zeroth Law -- Single-System Entropy -- Entropy -- Temperature -- Cycles and Comparisons of Versions of the Second Law -- A Geometric Route to Entropy and Temperature -- Phase Transitions and Critical Phenomena -- Non-Equilibrium Theory.

The aim of this text is to provide an account of the fundamentals of thermodynamics which is accessible at graduate level to physicists, mathematicians and philosophers of physics. The bulk of the book (Chapters 2-9) is based on the algebraic approach of Lieb and Yngvason, but extended to encompass both positive and negative temperatures and systems in which entropy increases and decreases in adiabatic processes. We show that these four possibilities are already present in Carathéodory's version of the Second Law which arises as a theorem from the axioms. We develop generalized versions of the Kelvin-Planck and Clausius formulations valid for the same range of systems. The parallel development in Chapter 10 takes a geometric approach. We discuss the limitations associated with the local nature of Carathéodory's Principle and present the resolution of this problem due to Boyling. Part of the aim here is to substantiate the claim of Arnold that the mathematical structure of thermodynamics is contact geometry. The last two chapters of the book extend the scope of the discussion to, respectively, critical phenomena and non-equilibrium systems. Chapter 11 is a presentation of phase transitions and critical phenomena in which we discuss universality and use scaling theory to derive scaling laws. Chapter 12 contains a generalization to non-equilibrium. We present the extension of Lieb and Yngvason's work to non-equilibrium and also give a brief account of classical irreversible thermodynamics (CIT). The latter enables a possible understanding of the way that the lack of a unique entropy function in the Lieb and Yngvason non-equilibrium approach can be resolved. The book is completed by a set of appendices which provide mathematical and physical support to the work in the main text.

ISBN: 9783031779480

Standard No.: 10.1007/978-3-031-77948-0doiSubjects--Topical Terms:

768900
Theoretical, Mathematical and Computational Physics.

LC Class. No.: QC311

Dewey Class. No.: 536.7

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520 $a The aim of this text is to provide an account of the fundamentals of thermodynamics which is accessible at graduate level to physicists, mathematicians and philosophers of physics. The bulk of the book (Chapters 2-9) is based on the algebraic approach of Lieb and Yngvason, but extended to encompass both positive and negative temperatures and systems in which entropy increases and decreases in adiabatic processes. We show that these four possibilities are already present in Carathéodory's version of the Second Law which arises as a theorem from the axioms. We develop generalized versions of the Kelvin-Planck and Clausius formulations valid for the same range of systems. The parallel development in Chapter 10 takes a geometric approach. We discuss the limitations associated with the local nature of Carathéodory's Principle and present the resolution of this problem due to Boyling. Part of the aim here is to substantiate the claim of Arnold that the mathematical structure of thermodynamics is contact geometry. The last two chapters of the book extend the scope of the discussion to, respectively, critical phenomena and non-equilibrium systems. Chapter 11 is a presentation of phase transitions and critical phenomena in which we discuss universality and use scaling theory to derive scaling laws. Chapter 12 contains a generalization to non-equilibrium. We present the extension of Lieb and Yngvason's work to non-equilibrium and also give a brief account of classical irreversible thermodynamics (CIT). The latter enables a possible understanding of the way that the lack of a unique entropy function in the Lieb and Yngvason non-equilibrium approach can be resolved. The book is completed by a set of appendices which provide mathematical and physical support to the work in the main text.
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