Thermal fluctuations of charged black holes in gravity's rainbow

Quantum fluctuation effects have an irrefutable role in high-energy physics. Such fluctuation can be often regarded as a correction of the infrared (IR) limit. In this paper, the effects of the first-order correction of entropy, caused by thermal fluctuation, on the thermodynamics of charged black holes in gravity's rainbow will be discussed. It will be shown that such correction has profound contributions to the high-energy limit of thermodynamical quantities and the stability conditions of black holes, and, interestingly, has no effect on thermodynamical phase transitions. The coupling between gravity's rainbow and the first-order correction will be addressed. In addition, the measurement of entropy as a function of fluctuation of temperature will be covered, and it will be shown that the de Sitter case enforces an upper limit on the values of temperature and produces cyclic-like diagrams, while for the anti-de Sitter case, a lower limit on the entropy is provided; although for special cases a cyclic-like behavior could be observed, no upper or lower limit exists for the temperature. In addition, a comparison between non-correction and correction-included cases on the thermodynamical properties of solutions will also be discussed and the effects of the first-order correction will be highlighted. It will be shown that the first-order correction provides solutions with larger classes of thermal stability conditions, which may result in the existence of a larger number of thermodynamical structures for the black holes.