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In this paper, we investigate the combined effects of the cloud of stringsand quintessence on the thermodynamics of a Reissner-Nordstr\"om-de Sitterblack hole. Based on the equivalent thermodynamic quantities considering thecorrelation between the black hole horizon and the cosmological horizon, weextensively discuss the phase transitions of the space-time. Our analysis provethat similar to the case in AdS space-time, second-order phase transitionscould take place under certain conditions, with the absence of first-orderphase transition in the charged de Sitter black holes with cloud of string andquintessence. The effects of different thermodynamic quantities on the phasetransitions are also quantitatively discussed, which provides a new approach tostudy the thermodynamic qualities of unstable dS space-time. Focusing on theentropy force generated by the interaction between the black hole horizon andthe cosmological horizon, as well as the Lennard-Jones force between twoparticles, our results demonstrate the strong degeneracy between the entropyforce of the two horizons and the ratio of the horizon positions, which followsthe surprisingly similar law given the relation between the Lennard-Jones forceand the ratio of two particle positions. Therefore, the study of the entropyforce between two horizons, is not only beneficial to the deep exploration ofthe three modes of cosmic evolution, but also helpful to understand thecorrelation between the microstates of particles in black holes and those inordinary thermodynamic systems.

Phase transitions and entropy force of charged de Sitter black holes with cloud of string and quintessence