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Axiomatic Relation between Thermodynamic and Information-Theoretic Entropies.
Mirjam Weilenmann1,2, Lea Kraemer1, Philippe Faist1,3
1Institute for Theoretical Physics, ETH Zurich, 8093 Switzerland.
This study links thermodynamic entropy (Clausius) and information entropy (Shannon), revealing a direct relationship between macroscopic heat measurements and uncertainty. This connection extends to quantum systems and nonequilibrium thermodynamics.
Area of Science:
- Thermodynamics
- Information Theory
- Statistical Mechanics
Background:
- Thermodynamic entropy (Clausius) describes macroscopic systems using heat and temperature.
- Information entropy (Shannon) quantifies uncertainty in data and probability distributions.
Purpose of the Study:
- To establish a direct connection between thermodynamic and information-theoretic entropy.
- To explore the implications for quantum systems and nonequilibrium thermodynamics.
Main Methods:
- Utilized an axiomatic framework for thermodynamics.
- Derived a direct relation between Clausius entropy and Shannon entropy (and von Neumann entropy for quantum systems).
Main Results:
- Established a quantitative link between Clausius entropy and Shannon entropy.
- Demonstrated that nonequilibrium thermodynamic entropy measures correspond to one-shot information theory entropies.
Conclusions:
- The study bridges classical thermodynamics with modern information theory.
- Provides a unified perspective on entropy across different scientific domains.
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