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Statistical physics of the symmetric group.
1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
Physical Review. E
|May 17, 2017
Summary
This study explores statistical physics models using permutations of ordered lists, like amino acid chains. It reveals novel behaviors and five distinct physical regimes in these systems.
Area of Science:
- Statistical Physics
- Systems Biology
- Combinatorics
Background:
- Biological cells utilize ordered chains, such as amino acids, where function depends on sequence.
- Understanding the statistical physics of sequence-dependent systems is crucial for biology.
Purpose of the Study:
- To investigate statistical physics models with state spaces defined by permutations of ordered lists.
- To analyze systems where energy depends on deviation from a correct ordering.
Main Methods:
- Theoretical study of systems with state spaces based on the symmetric group.
- Application of mean-field model with various parameter choices.
Main Results:
- Identified novel behaviors in systems with nonfactorizable state spaces.
- Discovered five distinct physical regimes characterized by two transition temperatures, a triple point, and a quadruple point.
Conclusions:
- The developed analysis provides a framework for understanding sequence-dependent systems in statistical mechanics.
- The approach can be extended to more complex combinatorial state spaces and other statistical mechanics problems.
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