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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.

Geometric Aspects and Some Uses of Deformed Models of Thermostatistics