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Microcanonical origin of the maximum entropy principle for open systems
1Department of Bioinformatics and Life Science, Soongsil University, Seoul 156-743, Korea. jul@ssu.ac.kr
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2012
Summary
This study demonstrates the equivalence between two methods for deriving the canonical ensemble, a fundamental concept in statistical mechanics. It shows how the maximum entropy principle naturally leads to the canonical distribution, even for dynamical systems.
Area of Science:
- Statistical Mechanics
- Thermodynamics
- Quantum Information Theory
Background:
- Two primary methods exist for deriving the canonical ensemble: as a limit of the microcanonical ensemble or via the maximum entropy principle.
- Understanding the canonical ensemble is crucial for describing systems in thermal equilibrium.
- The relationship between these two derivation methods has been a subject of theoretical interest.
Purpose of the Study:
- To demonstrate the equivalence of the microcanonical limit and maximum entropy approaches for deriving the canonical ensemble.
- To provide a unified framework for understanding canonical distribution.
- To extend the findings to justify path entropy maximization in dynamical systems.
Main Methods:
- Applied the maximum entropy formulation to a closed universe model comprising an open system and its surrounding bath.
- Performed partial maximization of entropy over the bath's degrees of freedom.
- Extended the mathematical formalism to analyze dynamical paths beyond equilibrium ensembles.
Main Results:
- Showed that the target function for the canonical distribution naturally arises from partial entropy maximization over the bath.
- Established the equivalence between the two distinct approaches for deriving the canonical ensemble.
- Provided a new justification for the principle of path entropy maximization.
Conclusions:
- The microcanonical and maximum entropy methods for deriving the canonical ensemble are equivalent.
- Partial entropy maximization offers a unified perspective on canonical distribution.
- The study offers a novel theoretical foundation for path entropy maximization in non-equilibrium statistical mechanics.
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