Internal energy of the medium formed in pp collisions

Abstract In this paper, we perform a thermostatistical analysis of the charged particles produced in minimum bias pp collisions across different energies available at the LHC-CERN reported by the ALICE Collaboration. To this end, we adopted the normalized $$p_\\text {T}$$ p T spectrum as the probability density function governing the $$p_\\text {T}$$ p T microstates of the produced hadrons, from which we can compute the entropy following the Shannon definition or the average $$p_\\text {T}$$ p T as the Bjorken-type energy estimator. Additionally, we estimate the temperature from the slope of the $$p_\\text {T}$$ p T spectrum at low $$p_\\text {T}$$ p T values. We use the Hagedorn and Tricomi functions to describe the $$p_\\text {T}$$ p T spectrum within a nonextensive approach and determine consistent thermodynamic frameworks by solving the fundamental relation $$dE/dT=C$$ d E / d T = C , where $$C=TdS/dT$$ C = T d S / d T is the heat capacity. We found that the internal energy behaves nonlinearly at LHC energies, indicating that the count of degrees of freedom is more complex than simply adding the number of flavors present in the hadron production. The main implication of our results is that the systems produced in pp collisions depart from the ideal gas picture and explain why the production of high $$p_\\text {T}$$ p T hadrons has always been observed, even in earlier experiments, which may also encompass other experiments colliding e $$^-$$ - p or e $$^+$$ + e $$^-$$ - .