Thermodynamic descriptions of polytropic gas and its viscous type as dark energy candidates

In this paper, at first, we focus on a Friedmann-Robertson-Walker (FRW) universe in which the dark energy candidate satisfies the polytropic equation of state and study thermodynamics of dark energy. Bearing the thermal fluctuation theorem in mind, we establish a relation between the thermal fluctuation of the system and mutual interaction between the dark energy and dark matter. Generalization to a viscous polytropic gas is also investigated. We point to a condition for decaying the dark energy candidate into the dark matter needed for alleviating the coincidence problem. The effects of dark energy candidates and their interactions with other parts of the cosmos on the horizon entropy as well as the second law of thermodynamics are also addressed. Our study suggests a correction term besides the Bekenstein entropy, which carries the information of the dark energy candidate, its interaction with other parts of the cosmos, and its viscosity.