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Zeroth law compatibility of nonadditive thermodynamics
1Department of Theoretical Physics, KFKI Research Institute for Particle and Nuclear Physics, Budapest, Hungary.
Summary
Nonextensive thermodynamics faces challenges with nonadditive composition rules violating the zeroth law. This study identifies compatible rules, finding that logarithms of quantities satisfy thermodynamic laws, resolving equilibrium questions.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Nonextensive Systems
Background:
- Nonextensive thermodynamics is criticized for incompatibility with the zeroth law when using nonadditive composition rules.
- The zeroth law is fundamental for defining thermal equilibrium and temperature.
- Existing frameworks struggle with equilibrium between systems exhibiting different nonextensivity parameters.
Purpose of the Study:
- To determine the general functional form of nonadditive composition rules compatible with the zeroth law of thermodynamics.
- To provide a theoretical basis for reconciling nonextensive systems with fundamental thermodynamic principles.
- To address long-standing questions regarding equilibrium in systems with varying nonextensivity.
Main Methods:
- Mathematical derivation of composition rules satisfying the zeroth law.
- Analysis of the functional form of these rules in relation to thermodynamic quantities.
- Application of standard thermodynamic relations to transformed quantities.
Main Results:
- The general functional form compatible with the zeroth law is additive for the formal logarithms of the original quantities.
- Familiar thermodynamic relations are shown to apply to these logarithmic transformations.
- This finding establishes a consistent framework for nonadditive composition rules.
Conclusions:
- The study resolves the conflict between nonextensive thermodynamics and the zeroth law by identifying specific composition rules.
- The use of logarithmic transformations provides a pathway to apply standard thermodynamic laws to nonextensive systems.
- This work offers a potential solution for understanding equilibrium in complex systems with differing nonextensivity.
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