Book contents
- The Arrow of Time
- The Arrow of Time
- Copyright page
- Contents
- Contributors
- Preface
- Acknowledgments
- Part I Local Systems
- 1 The Direction of Time: From the Cosmos to Local Systems
- 2 Thermodynamics with and without Irreversibility
- 3 Thermodynamics without Time
- Part II The Arrow of Time and Philosophical Issues
- Part III The Arrow of Time and Time-Reversal Invariance
- Part IV The Whole Universe
- Index
- References
2 - Thermodynamics with and without Irreversibility
from Part I - Local Systems
Published online by Cambridge University Press: aN Invalid Date NaN
Book contents
- The Arrow of Time
- The Arrow of Time
- Copyright page
- Contents
- Contributors
- Preface
- Acknowledgments
- Part I Local Systems
- 1 The Direction of Time: From the Cosmos to Local Systems
- 2 Thermodynamics with and without Irreversibility
- 3 Thermodynamics without Time
- Part II The Arrow of Time and Philosophical Issues
- Part III The Arrow of Time and Time-Reversal Invariance
- Part IV The Whole Universe
- Index
- References
Summary
Working inside the control-theoretic framework for understanding thermodynamics, I develop a systematic way to characterize thermodynamic theories via their compatibility with various notions of coarse-graining, which can be thought of as parametrizing an agent’s degree of control of a system’s degrees of freedom, and explore the features of those theories. Phenomenological thermodynamics is reconstructed via the ‘equilibration’ coarse-graining where a system is coarse-grained to a canonical distribution; finer-grained forms of thermodynamics differ from phenomenological thermodynamics only in that some states of a system possess a free energy that can be extracted by reversibly transforming the system (as close as possible) to a canonical distribution. Exceeding the limits of phenomenological thermodynamics thus requires both finer-grained control of a system and finer-grained information about its state. I consider the status of the second law in this framework, and distinguish two versions: the principle that entropy does not decrease, and the Kelvin/Clausius statements about the impossibility of transforming heat to work, or moving heat from a cold body to a hotter body, in a cyclic process. The former should be understood as relative to a coarse-graining, and can be violated given finer control than that coarse-graining permits; the latter is absolute and binds any thermodynamic theory compatible with the laws of physics, even the entirely reversible limit where no coarse-graining is appealed to at all. I illustrate these points via a discussion of Maxwell’s demon.
Information
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- Chapter
- Information
- The Arrow of TimeFrom Local Systems to the Whole Universe, pp. 12 - 55Publisher: Cambridge University PressPrint publication year: 2025
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