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Temperature gradients in equilibrium: Small microcanonical systems in an external field
Alberto Salazar1, Hernán Larralde2, François Leyvraz2
1Instituto de Ciencias Físicas, UNAM, Apartado Postal 48-3, Codigo Postal 62251, Cuernavaca, Morelos, Mexico and Instituut voor Theoretische Fysica, KU Leuven, Leuven, Belgium.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 11, 2014
Summary
In statistical mechanics, the microcanonical ensemble reveals that kinetic temperature varies with height in a small gaseous system under an external field, unlike the canonical ensemble. This effect is pronounced in mixtures of interacting particles.
Area of Science:
- Statistical Mechanics
- Thermodynamics
- Physical Chemistry
Background:
- Canonical ensemble in statistical mechanics predicts constant kinetic temperature and barometric density profiles for systems in external fields.
- Small gaseous systems under external fields exhibit unique thermodynamic behaviors not fully captured by standard ensemble averages.
Purpose of the Study:
- To investigate the behavior of kinetic temperature in small gaseous systems under a constant external field using the microcanonical ensemble.
- To analyze the height-dependent temperature profiles and inter-species temperature differences in such systems.
- To demonstrate these phenomena using a specific mechanical model.
Main Methods:
- Analysis of statistical mechanics in the microcanonical ensemble for a small gaseous system.
- Development and study of a Lorentz Gas model with interacting particles and spinning disks under a constant external force.
- Derivation of kinetic temperature profiles as a function of height and particle number (N).
Main Results:
- In the microcanonical ensemble, kinetic temperature is not constant with height for field-affected particles; it generally decreases with a gradient of order 1/N.
- For a mixture of field-influenced and field-uninfluenced species, kinetic temperatures differ even at the same height.
- The Lorentz Gas model confirms height-dependent particle temperature and height-independent disk temperature, highlighting a thermal disequilibrium.
Conclusions:
- The microcanonical ensemble reveals crucial deviations from canonical ensemble predictions regarding temperature profiles in small, externally-driven systems.
- Height-dependent kinetic temperature and inter-species thermal differences are significant phenomena in systems with external fields.
- The study highlights the importance of ensemble choice and system-specific models for accurately describing thermodynamic properties.
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