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Thermodynamics with long-range interactions: from Ising models to black holes
1Racah Institute of Theoretical Physics, Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel.
Summary
This study introduces methods to analyze thermodynamics in systems with long-range interactions, revealing nonextensive entropies. A novel lattice model demonstrates black hole-like properties, offering insights into thermodynamics and general relativity.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- General Relativity
Background:
- Systems with long-range interactions often exhibit nonextensive entropies.
- Understanding these systems is crucial for fields like astrophysics and condensed matter physics.
- Existing models may not fully capture the thermodynamic behavior of such complex systems.
Purpose of the Study:
- To develop methods for analyzing the thermodynamics of systems with long-range interactions.
- To investigate the nonextensivity of entropy in these systems.
- To explore analogies between these systems and concepts in general relativity, including black holes.
Main Methods:
- Development of analytical methods to calculate the degree of nonextensivity.
- Study of a lattice model with long-range spin-spin coupling.
- Analysis of a gravitating perfect fluid with constant density.
Main Results:
- Systems with long-range interactions show nonextensive entropies.
- A parameter akin to global temperature exists, alongside a local temperature.
- A lattice model exhibits black hole-like thermodynamic properties (temperature and entropy).
- Entropy scaling transitions from volume-based to area-based with increasing interaction strength in gravitating fluids.
Conclusions:
- The presented methods enable the analysis of nonextensive thermodynamics in systems with long-range interactions.
- The findings suggest a deep connection between statistical mechanics of long-range systems and general relativity.
- The black hole analog model provides a new framework for studying quantum gravity and black hole thermodynamics.
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