The heat death paradox, also known as thermodynamic paradox, Clausius' paradox, and Kelvin's paradox, is a ''

reductio ad absurdum In logic, (Latin for "reduction to absurdity"), also known as (Latin for "argument to absurdity") or ''apagogical argument'', is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absur ...

'' argument that uses

thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...

to show the impossibility of an infinitely old universe. It was formulated in February 1862 by

Lord Kelvin William Thomson, 1st Baron Kelvin (26 June 182417 December 1907), was a British mathematician, Mathematical physics, mathematical physicist and engineer. Born in Belfast, he was the Professor of Natural Philosophy (Glasgow), professor of Natur ...

and expanded upon by

Hermann von Helmholtz Hermann Ludwig Ferdinand von Helmholtz (; ; 31 August 1821 – 8 September 1894; "von" since 1883) was a German physicist and physician who made significant contributions in several scientific fields, particularly hydrodynamic stability. The ...

and

William John Macquorn Rankine William John Macquorn Rankine (; 5 July 1820 – 24 December 1872) was a Scottish mathematician and physicist. He was a founding contributor, with Rudolf Clausius and William Thomson (Lord Kelvin), to the science of thermodynamics, particularl ...

The paradox

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 The second law of thermodynamics is a physical law based on Universal (metaphysics), universal empirical observation concerning heat and Energy transformation, energy interconversions. A simple statement of the law is that heat always flows spont ...

postulated by

Rudolf Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Sadi Carnot's principle ...

and

, 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 Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...

. For two objects at the same temperature as much

heat flow Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, ...

s 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 In thermodynamics, the thermodynamic free energy is one of the state functions of a thermodynamic system. The change in the free energy is the maximum amount of work that the system can perform in a process at constant temperature, and its ...

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 Kelvin Zero, and it is possible that a maximum entropy state will be reached.
Laws of Thermodynamics
' Thompson and Clausius,

Oxford University Press Oxford University Press (OUP) is the publishing house of the University of Oxford. It is the largest university press in the world. Its first book was printed in Oxford in 1478, with the Press officially granted the legal right to print books ...

, 2015

Kelvin's solution

In February 1862, Lord Kelvin used the existence of the

Sun The Sun is the star at the centre of the Solar System. It is a massive, nearly perfect sphere of hot plasma, heated to incandescence by nuclear fusion reactions in its core, radiating the energy from its surface mainly as visible light a ...

and the

star A star is a luminous spheroid of plasma (physics), plasma held together by Self-gravitation, self-gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night sk ...

s as an empirical proof that the universe has not achieved

thermodynamic equilibrium Thermodynamic equilibrium is a notion of thermodynamics with axiomatic status referring to an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable ...

, 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 the

Big Bang The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models based on the Big Bang concept explain a broad range of phenomena, including th ...

or its successful Lambda-CDM refinement, which posit that the universe began roughly 13.8 billion years ago, not long enough ago for the universe to have approached thermodynamic equilibrium. Some proposed further refinements, termed eternal inflation, restore Kelvin's idea of unending time in the more complicated form of an eternal, exponentially-expanding multiverse in which mutually-inaccessible baby universes, some of which resemble the universe we inhabit, are continually being born.

Related paradoxes

Olbers' paradox file:Olbers' Paradox - All Points.gif, As more distant stars are revealed in this animation depicting an infinite, homogeneous, and static universe, they fill the gaps between closer stars. Olbers's paradox says that because the night sky is d ...

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 Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe, the cosmos. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', with the meaning of "a speaking of the wo ...

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.

References

{{DEFAULTSORT:Heat death paradox Thermodynamics Physical paradoxes Physical cosmology 1862 introductions

The paradox

Kelvin's solution

Modern cosmology

Related paradoxes

See also

References