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Relations between heat exchange and Rényi divergences
1School of Physics and Energy, Shenzhen University, Shenzhen 518060, China.
Physical Review. E
|May 16, 2018
Summary
We found an exact relation connecting heat exchange in thermodynamic systems to Rényi divergences. This quantifies heat statistics using divergences between initial equilibrium and final nonequilibrium states.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Quantum Information Theory
Background:
- Understanding heat exchange in thermodynamic systems is crucial.
- Characterizing nonequilibrium states is a key challenge in statistical mechanics.
- Rényi divergences offer a powerful tool for quantifying differences between probability distributions.
Purpose of the Study:
- To establish an exact relation between heat exchange and Rényi divergences.
- To quantify statistical moments of heat exchange using information-theoretic quantities.
- To provide a unified framework applicable to both classical and quantum systems.
Main Methods:
- Derivation of an exact mathematical relation.
- Application of Rényi divergences to thermodynamic equilibrium and nonequilibrium states.
- Analysis of heat statistics moments.
Main Results:
- An exact relation is established connecting heat exchange to Rényi divergences.
- Moments of heat statistics are shown to be determined by Rényi divergences.
- Average heat exchange is quantified by the relative entropy.
Conclusions:
- The derived relation provides a novel way to understand heat exchange in nonequilibrium processes.
- Rényi divergences serve as a fundamental measure for heat statistics.
- The findings are applicable to a broad range of finite classical and quantum systems.
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