Heat death paradox

The paradox

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. The 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. If the universe were infinitely old, there must have been enough time for the stars to cool and warm their surroundings. Everywhere should therefore be at the same temperature and there should either be no stars, or everything should be as hot as stars. The universe should thus achieve, or asymptotically tend to, thermodynamic equilibrium, which corresponds to a state where no thermodynamic free energy is left, and therefore no further work is possible: this is the heat death of the universe, as predicted by Lord Kelvin in 1852. The average temperature of the cosmos should also asymptotically tend to absolute zero, and it is possible that a maximum entropy state will be reached.