Geometric Aspects and Some Uses of Deformed Models of Thermostatistics

Abstract

We consider diverse deformed Bose gas models (DBGMs) focusing on distributions and correlations of any order, and also on deformed thermodynamics. For so-called μ -deformed Bose gas model ( μ -DBGM), main thermodynamic aspects are treated: total number of particles, deformed partition function, etc. Using a geometric approach, we confirm the existence of critical behavior—Bose-like condensation; we find the critical temperature T c ( μ ) depending on μ so that T c ( μ ) > T c ( Bose ) for μ > 0 . This fact and other advantages of μ -DBGM relative to the usual Bose gas, e.g., stronger effective inter-particle attraction (controlled by the parameter μ ), allow us to consider the condensate in μ -DBGM as a candidate for modeling dark matter. As another, quite successful application we discuss the usage of the two-parameter ( μ ˜ , q )-deformed BGM for effective description of the peculiar (non-Bose like) behavior of two-pion correlations observed in the STAR experiment at RHIC (Brookhaven). Herein, we point out the transparent role of the two deformation parameters μ ˜ and q as being responsible for compositeness and (effective account of) interactions of pions, respectively.

Keywords

• deformed Bose gas models
• thermodynamic geometry
• critical temperature
• condensate
• dark matter
• higher-order distributions
• correlation function intercept
• two-pion correlations
• RHIC/STAR experiment