The heat death paradox, also known as thermodynamic paradox, Clausius' paradox and Kelvin’s paradox, is a reductio ad absurdum argument that uses thermodynamics to show the impossibility of an infinitely old universe. It was formulated in February 1862 by Lord Kelvin and expanded upon by Hermann von Helmholtz and William John Macquorn Rankine. Assuming that the universe is eternal, a question arises: How is it that thermodynamic equilibrium has not already been achieved? This theoretical paradox is directed at the then-mainstream strand of belief in a classical view of a sempiternal universe, whereby its matter is postulated as everlasting and having always been recognisably the universe. Heat death paradox is born of a paradigm resulting from fundamental ideas about the cosmos. It is necessary to change the paradigm to resolve the paradox. The paradox was based upon the rigid mechanical point of view of the second law of thermodynamics postulated by Rudolf Clausius and Lord Kelvin, according to which heat can only be transferred from a warmer to a colder object. It notes: if the universe were eternal, as claimed classically, it should already be cold and isotropic (its objects should have the same temperature, and the distribution of matter or radiation should be even). Kelvin compared the universe to a clock that runs slower and slower, constantly dissipating energy in impalpable heat, although he was unsure whether it would stop for ever (reach thermodynamic equilibrium). According to this model, the existence of usable energy, which can be used to perform work and produce entropy, means that the clock has not stopped - since a conversion of heat in mechanical energy (which Kelvin called a rejuvenating universe scenario) is not contemplated. According to the laws of thermodynamics, any hot object transfers heat to its cooler surroundings, until everything is at the same temperature. For two objects at the same temperature as much heat flows from one body as flows from the other, and the net effect is no change.
Karim Achouri, Christophe Caloz