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Why Noether's theorem applies to statistical mechanics
Sophie Hermann1, Matthias Schmidt1
1Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95447 Bayreuth, Germany.
Summary
Noether's theorem, typically used for mechanics and field theory, is extended to thermal systems. This framework reveals connections between symmetries and conservation laws in statistical mechanics, even for active particles.
Area of Science:
- Statistical Mechanics
- Theoretical Physics
- Symmetry Principles
Background:
- Noether's theorem classically links conservation laws to symmetries.
- Existing applications focus on particle mechanics and field theory.
- Thermal systems require a statistical mechanical description due to paramount fluctuations.
Purpose of the Study:
- Extend Noether's theorem to thermal systems.
- Provide a pedagogical introduction using the canonical ensemble.
- Apply the framework to ideal sedimentation and active Brownian particles.
Main Methods:
- Viewing thermodynamic quantities like free energy as functionals.
- Employing systematic functional differentiation.
- Analyzing macroscopic average forces and molecular correlations.
Main Results:
- Demonstrated Noether's theorem's applicability to thermal systems.
- Derived identities relating symmetries to conservation laws in statistical mechanics.
- Extended the analysis to systems out-of-equilibrium and active matter.
Conclusions:
- Noether's theorem provides a unified framework for conservation laws in diverse physical systems.
- Functional methods offer a powerful approach for analyzing complex many-body systems.
- The findings have implications for understanding both equilibrium and non-equilibrium statistical mechanics.
Keywords:
Noether’s theoremdensity functional theoryinvarianceliquid state theorypower functional theorystatistical mechanicssum rulesMore Related Videos
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