Thermal fluctuations of charged C-metric accelerating black holes with cosmological constant

In this paper, we study thermal fluctuations of C$-$Metric Black Holes (BHs) with charge, cosmological constant and accelerating parameter. We first derive modified expressions for logarithmic corrections to the entropy, which yield leading-order corrections to thermodynamic quantities such as Hawking temperature, mass, Helmholtz function, Gibbs energy, heat capacity and volumes. It is found that the logarithmic corrections change their form under the influence of thermal fluctuations. We also discuss the phase transition and thermal stability of these quantities for the accelerating black holes with cosmological constant. In this context, the presence of first-order corrections to the first law makes it possible to observe a phase transition from an unstable to a stable state. In addition, we explore the efficiency of the system when treated as a heat engine, taking into account the influence of the acceleration parameter A, charge e, and cosmological constant. Furthermore, we examine the Joule-Thomson coefficient and determine the corresponding inversion temperature.