I would like to make a stand regarding the topic of entropy reversal. Entropy CAN in fact be reduced in a closed system, and this happens spontaneously according to the fluctuation theorem. Its been published in a well known scientific journal over a decade ago, and beforehand has been established by many notable physicist. Take for instance the case of a particle suspended in a liquid. The particle will rise and fall in the liquid column thus gaining and losing energy, which comes from thermal energy of brownian motion. The system will cool when the particle rises and it will warm up when the particle descends. No matter how large the number of particles is, at equilibrium there is an equal chance that the system's entropy will increase and decrease/ system will heat or cool.