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The idea of the heat death of the universe, proposed in 1851 by [[w:William Thomson, 1st Baron Kelvin|William Thomson]], stems from the [[second law of thermodynamics]], which states that [[heat]] tends to pass from hotter to colder bodies and eventually becomes uniformly distributed. As an elementary particle of matter (such as a proton) self‑gravitationally shrinks, its heat becomes intensified ("augmented") to a higher temperature and then radiated away into the ambient vacuum:
<blockquote>
Although mechanical energy is indestructible, there is a universal tendency to its dissipation, which produces throughout the system a gradual '''augmentation''' and diffusion of heat, cessation of motion and exhaustion of the potential energy of the material Universe.
:—Thomson, William. [http://zapatopi.net/kelvin/papers/on_the_age_of_the_suns_heat.html On the Age of the Sun’s Heat] ''Macmillan's Magazine'', 5&nbsp;March 1862, pp. 388–93
</blockquote>

==Mechanism of heat death==
Initially, the universe has the maximal (''i.e.'', zero) [[potential energy]], and the minimal (''i.e.'', zero) actual energy. Such a universe is in a state of '''heat death''' and exists as a uniform blanket of zero-temperature heat. According to the [[second law of thermodynamics]], heat tends to pass from hotter to colder bodies. So, when a portion of the zero&#8209;temperature heat self&#8209;gravitationally shrinks to a nonzero temperature, a half of the resultant nonzero&#8209;temperature heat becomes radiated into the colder ambient vacuum, at which moment the particle of nonzero&#8209;temperature heat undergoes self&#8209;gravitational shrinkage to a still higher temperature.<ref>Böhm-Vitense, Erika. [https://books.google.co.ukm/books?id=msZMEvEpxG8C&pg=PA29 Introduction to Stellar Astrophysics]. CUP, 1992, p. 29. "After each infinitesimal step of collapse the star has to wait until it has radiated away a half of the released gravitational energy before it can continue to contract."</ref> Thus the temperature difference between the self&#8209;gravitationally shrinking particle and the ambient vacuum increases, which increases the rate of heat loss and thereby accelerates the particle's self&#8209;gravitational shrinkage:
<blockquote>
<p>All change is relative. The universe is expanding relatively to our common material standards; our material standards are shrinking relatively to the size of the universe. The theory of the "expanding universe" might also be called the theory of the "shrinking atom". ...</p>
<p>Let us then take the whole universe as our standard of constancy, and adopt the view of a cosmic being whose body is composed of intergalactic spaces and swells as they swell. Or rather we must now say it keeps the same size, for he will not admit that it is he who has changed. Watching us for a few thousand million years, he sees us shrinking; atoms, animals, planets, even the galaxies, all shrink alike; only the intergalactic spaces remain the same. The earth spirals round the sun in an ever&#8209;decreasing orbit. It would be absurd to treat its changing revolution as a constant unit of time. The cosmic being will naturally relate his units of length and time so that the velocity of light remains constant. Our years will then decrease in geometrical progression in the cosmic scale of time. On that scale man's life is becoming briefer; his threescore years and ten are an ever&#8209;decreasing allowance. Owing to the property of geometrical progressions an infinite number of our years will add up to a finite cosmic time; so that what we should call the end of eternity is an ordinary finite date in the cosmic calendar. But on that date the universe has expanded to infinity in our reckoning, and we have shrunk to nothing in the reckoning of the cosmic being.</p>
We walk the stage of life, performers of a drama for the benefit of the cosmic spectator. As the scenes proceed he notices that the actors are growing smaller and the action quicker. When the last act opens the curtain rises on midget actors rushing through their parts at frantic speed. Smaller and smaller. Faster and faster. One last microscopic blurr of intense agitation. And then nothing.
:—Eddington, Arthur. [https://books.google.co.ukm/books?id=KHyV4-2EyrUC&pg=PA90 The Expanding Universe] CUP, 1933, pp.&nbsp;90–92
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When the above-described exponentially accelerating shrinkage and radiative "evaporation" of positive&#8209;actual&#8209;energy protons into the negative&#8209;potential&#8209;energy ambient vacuum comes to an end, the universe again has the maximal (''i.e.'', zero) potential energy, and the minimal (''i.e.'', zero) actual energy. Such a universe is in a state of '''heat death''' and exists as a uniform blanket of zero-temperature heat. The 13.8&#8209;billion&#8209;year&#8209;long gravitational life cycle then begins anew. And so ''ad infinitum''.
<center>***</center>
For stable equilibrium the gravitational potential energy of the system must be a minimum.<ref>Barker, George Frederick. [https://books.google.co.ukm/books?id=bKEAAAAAMAAJ&q=%22for+stable+equilibrium+the+potential+energy+of+the+system+must+be+a+minimum%22 Physics: Advanced Course]. Henry Holt, 1893, p. 202</ref> In the case of multiple protons, the gravitational potential energy is proportional to the radius of a single proton and to the spatial separation of protons.<ref>Thomson, it will be remembered, stores his heat in the form of the potential energy of separation of the elements of the sun.</ref> Thus, the continuum's protons attain the minimal potential energy by shrinking and accelerating towards the continuum's central proton:
<center>[[Image:Dendritic_drainage_system.jpg|200px]]</center>
As the peripheral protons move towards the continuum's central proton, whose accelerating influence intensifies in accordance with the [[Inverse-square law|inverse&#8209;square law]], they radiate away their rest mass, so that their resistance to acceleration decreases. Having radiated away a half of their initial rest mass, the peripheral protons instantaneously tunnel into the continuum's central proton.

==Evolution of the idea==
At first, the prevailing opinion was that the heat death of the universe was in the distant future, because stars initially had high temperatures and cooled progressively with time, so that the rate of heat loss exponentially decreased. This insouciant view was overturned by [[w:Jonathan Homer Lane|Jonathan Homer Lane]], who in 1870 discovered that the temperature of a self&#8209;gravitating perfect-gas sphere is inversely proportional to its radius: ''rT''(''r'')&nbsp;=&nbsp;''constant''. This equation is known as Lane's law.<ref>Reid, Neill I. Hawley, Suzanne L. [https://books.google.co.ukm/books?id=04_aBwAAQBAJ&pg=PA84 New Light on Dark Stars: Red Dwarfs, Low-Mass Stars, Brown Dwarfs]. Springer, 2013, p. 84</ref> For example, when the sphere's radius (''r'') decreases tenfold, the sphere's temperature (''T'') increases tenfold:
<blockquote>
Lane reached the apparently paradoxical result that a star by losing heat and contracting actually grew hotter. A star  shrinking under gravitation to half its linear size and remaining built on the same model, or "homologous" (i.e., the densities at two corresponding points at any two stages remaining the same fraction  of the mean density) would be eight times as dense, and the internal  pressures would be sixteen times as great as the overlying material  is attracted four times as strongly and its weight is held up on only a quarter of the area. From the formula connecting temperature with pressure and density, given earlier in the chapter, it will be seen that the temperature in this example would be twice as great. By such  reasoning, Lane concluded that as stars get smaller they grow hotter to withstand gravitation and resist collapse.
:—Doig, Peter. [https://www.archive.org/stream/outlineofstellar031648mbp#page/n95/mode/2up An Outline of Stellar Astronomy] Hutchinson, 1947, p. 76
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The [[Stefan–Boltzmann law]] (1879) dictates that the rate at which a unit surface area of the self&#8209;gravitationally condensing sphere radiates away heat is proportional to the fourth power of the sphere's temperature. So, even after taking into account that the sphere's surface area decreases a hundredfold (as the square of the radius), Lane's law implies that, '''when the self&#8209;gravitating sphere's radius shrinks tenfold, the sphere's total radiative heat loss per unit time increases a hundredfold'''.

In addition, the gravitational potential energy of a self&#8209;gravitationally collapsing uniform sphere is proportional to its radius ''R'':
:<math>U=-\frac{3GM^2}{5R}</math>
That is why the tenfold decrease in the radius implies that the amount of generated collapse&#8209;impeding actual energy decreases tenfold. Therefore, '''when the self&#8209;gravitating sphere's radius shrinks tenfold, the speed of the sphere's collapse increases a thousandfold'''.

In 1983, numerical calculations on large computers predicted that as the temperature is raised the colour&#8209;repelling physical vacuum should flip into the simple vacuum, of which protons consist, at a temperature of 2&nbsp;×&nbsp;10<sup>12</sup> K.<ref>Willis, Bill. [https://books.google.co.ukm/books?id=F0aIiC-z5_kC&pg=PA10 Collisions to melt the vacuum]. ''New Scientist'', 3 October 1983, p. 10</ref> From the [[Stefan–Boltzmann law]] it follows that a body as hot as the proton must be radiating away its energy at a frantic pace and shrink accordingly. To an observer consisting of such rapidly shrinking protons, intergalactic spaces must appear to be expanding with an exponential acceleration. In 1998, [[w:Adam Riess|Adam Riess]] and his team discovered that the apparent expansion of intergalactic spaces is accelerating. On 5 April 2016, Adam Riess ''et al.'' announced that the rate of the acceleration is itself increasing—over the three years since 21 March 2013, when the [[w:Planck (spacecraft)|Planck space observatory]] published the local [[Hubble's law|Hubble constant]] value, the apparent expansion of intergalactic spaces had accelerated by nine per cent more than expected.<ref>Hirsch, Arthur. [http://hub.jhu.edu/2016/06/03/universe-expanding-faster-than-predicted/ Our universe is expanding faster than scientists predicted, study suggests]. ''Hub'', 3 June 2016</ref> The proton's heat death is coming apace and hastening.

In 1974, [[Stephen Hawking]] applied the above&#8209;described principle of heat death to black holes and found that they, too, radiate away their energy ([[Hawking radiation]]) and consequently shrink in size; the smaller a black hole becomes, the faster it radiates away its remaining energy.

==Related pages==
*[[Minimum total potential energy principle]]

==References==
{{Reflist}}

[[Category:Cosmology]]
[[Category:Thermodynamics]]
[[Category:Universe]]