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 $q-1\ll 1$ 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.

Close

PrevNext

View figure in article

• Complex systems
• Nonequilibrium fluctuations
• Temperature
• Thermodynamics
• Perturbative methods