Complexity drives the symmetry breaking of temperature fluctuations

Abstract

Frequently, nonextensive systems are described through $q$-exponential functions, where the $q$-parameter determines how far a system is from equilibrium. In this work, we study systems constrained to $q-1\ll1$ to describe systems near thermal equilibrium, and derive the probability density function and temperature fluctuations. To this end, we derive the series expansion of the $q$-exponential function, yielding a perturbative series that is a superposition of gamma distributions. On the other hand, the temperature fluctuations are expressed as a superposition of Dirac delta functions and their derivatives, meaning that the bulk of the system remains at a constant temperature, while point-temperature variations emerge, marking the system's departure from thermal equilibrium. The statistics of the temperature fluctuations exhibit a transition from a symmetric to a nonsymmetric distribution as the nonextensive parameter increases. These results provide evidence of the association between the emergence of nonextensivity and the symmetry breaking of temperature fluctuations.