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Second law and entropy production in a nonextensive system.
Mauricio S Ribeiro1, Gabriela A Casas1, Fernando D Nobre1
1Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 14, 2015
Summary
This study investigates superconducting vortices using a nonlinear Fokker-Planck equation. Results show entropy increases over time, aligning with the second law of thermodynamics in nonextensive statistical mechanics.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Thermodynamics
Background:
- Type-II superconductors are often modeled using overdamped motion of superconducting vortices.
- This model has been recently linked to a nonlinear Fokker-Planck equation and nonextensive statistical mechanics, specifically the S(2)(t) entropy.
- Understanding the thermodynamic behavior of these systems is crucial for superconductor applications.
Purpose of the Study:
- To analyze the entropy time rate (dS(2)(t)/dt) for superconducting vortices under overdamped motion.
- To investigate both entropy production within the system and entropy flux to the surroundings.
- To validate the applicability of the nonlinear Fokker-Planck equation and nonextensive statistical mechanics framework to irreversible processes in superconductors.
Main Methods:
- Utilized a nonlinear Fokker-Planck equation derived from the overdamped motion model of superconducting vortices.
- Analyzed the entropy production and entropy flux during an irreversible process.
- Performed molecular dynamics simulations to compare with analytical predictions.
Main Results:
- Demonstrated good agreement between molecular dynamics simulations and analytical results.
- Confirmed that the second law of thermodynamics holds within the studied framework.
- Observed a consistent increase in the S(2)(t) entropy over time until a stationary state is reached.
Conclusions:
- The nonlinear Fokker-Planck equation provides a valid framework for describing the irreversible processes and thermodynamic behavior of superconducting vortices.
- The study confirms the increase of S(2)(t) entropy, supporting the second law of thermodynamics in this context.
- The findings contribute to a deeper understanding of nonextensive statistical mechanics applied to condensed matter systems.
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