Repulsive particles under a general external potential: Thermodynamics by neglecting thermal noise

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Thermodynamics

Background:

• Nonextensive statistical mechanics introduces generalized entropy (s_q) and effective temperature (θ).
• Previous work established a thermodynamic framework for q=2 using harmonic potentials and repulsively interacting vortices in superconductors.
• High effective temperatures in these systems allow neglecting thermal noise.

Purpose of the Study:

• To extend the thermodynamic framework to a more general confining potential, ϕ(x)=α|x|^z/z, where z>1.
• To verify if key thermodynamic results hold for this generalized potential.
• To explore the implications for systems like type-II superconductors.

Main Methods:

• Generalization of the thermodynamic framework to arbitrary confining potentials (z>1).
• Analysis of the effective temperature (θ) conjugated to the generalized entropy (s_2).
• Construction and analysis of a Carnot cycle with effective temperatures.
• Application of Legendre transformations to derive thermodynamic potentials, Maxwell relations, and response functions.

Main Results:

• The definition of effective temperature (θ) conjugated to entropy (s_2) remains valid for any z>1.
• A Carnot cycle was constructed with efficiency η=1-(θ_2/θ_1), independent of the potential's exponent z.
• Alternative thermodynamic potentials, Maxwell relations, and response functions were derived using Legendre transformations.

Conclusions:

• A consistent thermodynamic framework is established for a general confining potential.
• The results suggest broad applicability and increase the potential for experimental verification in systems exhibiting nonextensive behavior.