The average temperature of the cosmos should also asymptotically tend to Kelvin Zero, and it is possible that a maximum entropy state will be reached. Solution In February 1862, Lord Kelvin used the existence of the Sun and the stars as an empirical proof that the universe has not achieved thermodynamic equilibrium, as entropy production and free work are still possible, and there are temperature differences between objects. Helmholtz and Rankine expanded Kelvin’s work soon after. Since there are stars and colder objects, the universe is not in thermodynamic equilibrium, so it cannot be infinitely old. Modern cosmology The paradox does not arise in modern cosmology, which posits that the universe began in a Big Bang roughly 13.8 billion years ago – which is not long enough ago for the universe to have approached thermodynamic equilibrium. Related paradoxes Olbers' paradox is another paradox which aims to disprove an infinitely old static universe, but it only fits with a static universe scenario. Also, unlike Kelvin’s paradox, it relies on Cosmology rather than Thermodynamics. The Boltzmann Brain can also be related to Kelvin’s, as it focuses on the spontaneous generation of a brain (filled with false memories) from entropy fluctuations, in a universe which has been lying in a heat death state for an indefinite amount of time. See also Entropy (arrow of time) Graphical timeline from Big Bang to Heat Death Heat death of the universe List of paradoxes Olbers' paradox Thermodynamic temperature References Thermodynamics Physical paradoxes Physical cosmology 1862 introductions