Heat death paradox
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The heat death paradox, also known as Clausius paradox and thermodynamic paradox, is an argument attempting to use thermodynamics to make deductions about the nature of the universe. Specifically, it attempts to argue against an infinitely old, static model of the universe using reductio ad absurdum.
The argument holds that: If the universe were infinite in extent it would also have to be infinitely old.
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 paradox does not arise in steady state or chaotic inflationary cosmologies. They escape the paradox because they are expanding. Radiation is continually being red-shifted by the expansion, causing background cooling.
See also 
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