Statistical mechanics of systems with long-range interactions and negative absolute temperature

Area of Science:

• Statistical Mechanics
• Computational Physics

Background:

• Hamiltonian models with long-range interactions can exhibit unusual thermodynamic properties.
• Ensemble equivalence, a cornerstone of statistical mechanics, may break down under certain conditions, such as in systems with negative temperatures.

Purpose of the Study:

• To analytically and numerically investigate ensemble nonequivalence in a specific Hamiltonian model.
• To explore the behavior of thermodynamic quantities and distributions in the negative temperature regime.
• To verify the Fluctuation-Dissipation Theorem in regions of ensemble nonequivalence.

Main Methods:

• Analytical calculations to determine conditions for entropy behavior.
• Molecular dynamics simulations to reconstruct caloric curves and observe momentum distributions.
• Numerical verification of the Fluctuation-Dissipation Theorem.

Main Results:

• An energy interval was identified where microcanonical entropy decreases with energy, indicating ensemble nonequivalence.
• Simulations confirmed analytical predictions and revealed a generalized Maxwell-Boltzmann distribution for momenta.
• The Fluctuation-Dissipation Theorem was found to hold even at negative temperatures and in nonequivalent ensemble regions.

Conclusions:

• The study demonstrates ensemble nonequivalence in a long-range interacting Hamiltonian model, particularly at negative temperatures.
• The findings highlight the importance of considering ensemble-specific properties in statistical mechanics.
• The validity of the Fluctuation-Dissipation Theorem under these conditions provides further insight into the system's equilibrium properties.