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The heat death of the universe is a plausible ultimate fate of the universe in which the universe has diminished to a state of no thermodynamic free energy and therefore can no longer sustain processes that increase entropy. Heat death does not imply any particular absolute temperature; it only requires that temperature differences or other processes may no longer be exploited to perform work. In the language of physics, this is when the universe reaches thermodynamic equilibrium (maximum entropy).

If the topology of the universe is open or flat, or if dark energy is a positive cosmological constant (both of which are supported by current data), the universe will continue expanding forever and a heat death is expected to occur, with the universe cooling to approach equilibrium at a very low temperature after a very long time period.

The hypothesis of heat death stems from the ideas of William Thomson, 1st Baron Kelvin, who in the 1850s took the theory of heat as mechanical energy loss in nature (as embodied in the first two laws of thermodynamics) and extrapolated it to larger processes on a universal scale.

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‑temperature heat self‑gravitationally shrinks to a nonzero temperature, a half of the resultant nonzero‑temperature heat becomes radiated into the colder ambient vacuum, at which moment the particle of nonzero‑temperature heat undergoes self‑gravitational shrinkage to a still higher temperature. Thus the temperature difference between the self‑gravitationally shrinking particle and the ambient vacuum increases, which increases the rate of heat loss and thereby accelerates the particle's self‑gravitational shrinkage:

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". ...

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‑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‑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.

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.

When the above-described exponentially accelerating shrinkage and radiative "evaporation" of positive‑actual‑energy protons into the negative‑potential‑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‑billion‑year‑long gravitational life cycle then begins anew. And so ad infinitum.

For stable equilibrium the gravitational potential energy of the system must be a minimum. 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. Thus, the continuum's protons attain the minimal potential energy by shrinking and accelerating towards the continuum's central proton:

As the peripheral protons move towards the continuum's central proton, whose accelerating influence intensifies in accordance with the inverse-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.

Origins of the idea

The idea of heat death was first proposed in 1851 by William Thomson, 1st Baron Kelvin, who theorized further on the mechanical energy loss views of Sadi Carnot (1824), James Joule (1843), and Rudolf Clausius (1850). It 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 condensed ("augmented") to a higher temperature and then radiated away into the ambient vacuum:

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.

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 Jonathan Homer Lane, who in 1870 discovered that the temperature of a self‑gravitating perfect-gas sphere is inversely proportional to its radius: rT(r) = constant. This equation is known as Lane's law. For example, when the sphere's radius (r) decreases tenfold, the sphere's temperature (T) increases tenfold:

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.

The Stefan–Boltzmann law (1879) dictates that the rate at which a unit surface area of the self‑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‑gravitating sphere's radius shrinks tenfold, the sphere's total radiative heat loss per unit time increases a hundredfold.

In 1983, numerical calculations on large computers predicted that as the temperature is raised the colour‑repelling physical vacuum should flip into the simple vacuum, of which protons consist, at a temperature of 2 × 10 K. 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 exponential acceleration. On 5 April 2016, Adam Riess et al. announced that, over the three years since 21 March 2013, when the Planck space observatory published the local Hubble constant value, the apparent expansion of intergalactic spaces had unexpectedly accelerated by nine per cent. The proton's heat death is coming apace and hastening.

In 1974, Stephen Hawking applied the above‑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.

History

The idea of heat death of the universe derives from discussion of the application of the first two laws of thermodynamics to universal processes. Specifically, in 1851 William Thomson (Lord Kelvin) outlined the view, as based on recent experiments on the dynamical theory of heat, that "heat is not a substance, but a dynamical form of mechanical effect, we perceive that there must be an equivalence between mechanical work and heat, as between cause and effect."

In 1852, Thomson published On a Universal Tendency in Nature to the Dissipation of Mechanical Energy in which he outlined the rudiments of the second law of thermodynamics summarized by the view that mechanical motion and the energy used to create that motion will tend to dissipate or run down, naturally. The ideas in this paper, in relation to their application to the age of the sun and the dynamics of the universal operation, attracted the likes of William Rankine and Hermann von Helmholtz. The three of them were said to have exchanged ideas on this subject. In 1862, Thomson published "On the age of the Sun’s heat", an article in which he reiterated his fundamental beliefs in the indestructibility of energy (the first law) and the universal dissipation of energy (the second law), leading to diffusion of heat, cessation of useful motion (work), and exhaustion of potential energy through the material universe while clarifying his view of the consequences for the universe as a whole. In a key paragraph, Thomson wrote:

The result would inevitably be a state of universal rest and death, if the universe were finite and left to obey existing laws. But it is impossible to conceive a limit to the extent of matter in the universe; and therefore science points rather to an endless progress, through an endless space, of action involving the transformation of potential energy into palpable motion and hence into heat, than to a single finite mechanism, running down like a clock, and stopping for ever.

In the years to follow both Thomson’s 1852 and the 1865 papers, Helmholtz and Rankine both credited Thomson with the idea, but read further into his papers by publishing views stating that Thomson argued that the universe will end in a "heat death" (Helmholtz) which will be the "end of all physical phenomena" (Rankine).

Current status

Proposals about the final state of the universe depend on the assumptions made about its ultimate fate, and these assumptions have varied considerably over the late 20th century and early 21st century. In a hypothesized "open" or "flat" universe that continues expanding indefinitely, a heat death is expected to occur. If the cosmological constant is zero, the universe will approach absolute zero temperature over a very long timescale. However, if the cosmological constant is positive, as appears to be the case in recent observations, the temperature will asymptote to a non-zero, positive value and the universe will approach a state of maximum entropy.

The "heat death" situation could be avoided if there is a method or mechanism to regenerate hydrogen atoms from radiation, dark energy or other sources in order to avoid a gradual running down of the universe due to the conversion of matter into energy and heavier elements in stellar processes.

Time frame for heat death

From the Big Bang through the present day, matter and dark matter in the universe are thought to have been concentrated in stars, galaxies, and galaxy clusters, and are presumed to continue to be so well into the future. Therefore, the universe is not in thermodynamic equilibrium and objects can do physical work. The decay time for a supermassive black hole of roughly 1 galaxy-mass (10 solar masses) due to Hawking radiation is on the order of 10 years, so entropy can be produced until at least that time. After that time, the universe enters the so-called Dark Era, and is expected to consist chiefly of a dilute gas of photons and leptons. With only very diffuse matter remaining, activity in the universe will have tailed off dramatically, with extremely low energy levels and extremely long time scales. Speculatively, it is possible that the universe may enter a second inflationary epoch, or, assuming that the current vacuum state is a false vacuum, the vacuum may decay into a lower-energy state. It is also possible that entropy production will cease and the universe will reach heat death. Possibly another universe could be created by random quantum fluctuations or quantum tunneling in roughly ${\displaystyle 10^{10^{10^{56}}}}$ years. Over an infinite time, there would be a spontaneous entropy decrease via the Poincaré recurrence theorem, thermal fluctuations, and Fluctuation theorem.

Controversies

Max Planck wrote that the phrase 'entropy of the universe' has no meaning because it admits of no accurate definition. More recently, Grandy writes: "It is rather presumptuous to speak of the entropy of a universe about which we still understand so little, and we wonder how one might define thermodynamic entropy for a universe and its major constituents that have never been in equilibrium in their entire existence." According to Tisza: "If an isolated system is not in equilibrium, we cannot associate an entropy with it." Buchdahl writes of "the entirely unjustifiable assumption that the universe can be treated as a closed thermodynamic system". According to Gallavotti: "... there is no universally accepted notion of entropy for systems out of equilibrium, even when in a stationary state." Discussing the question of entropy for non-equilibrium states in general, Lieb and Yngvason express their opinion as follows: "Despite the fact that most physicists believe in such a nonequilibrium entropy, it has so far proved impossible to define it in a clearly satisfactory way." In the opinion of Čápek and Sheehan, "no known formulation applies to all possible thermodynamic regimes." In Landsberg's opinion, "The third misconception is that thermodynamics, and in particular, the concept of entropy, can without further enquiry be applied to the whole universe. ... These questions have a certain fascination, but the answers are speculations, and lie beyond the scope of this book."

A recent analysis of entropy states that "The entropy of a general gravitational field is still not known," and that "gravitational entropy is difficult to quantify." The analysis considers several possible assumptions that would be needed for estimates, and suggests that the visible universe has more entropy than previously thought. This is because the analysis concludes that supermassive black holes are the largest contributor. Another writer goes further; "It has long been known that gravity is important for keeping the universe out of thermal equilibrium. Gravitationally bound systems have negative specific heat—that is, the velocities of their components increase when energy is removed. ... Such a system does not evolve toward a homogeneous equilibrium state. Instead it becomes increasingly structured and heterogeneous as it fragments into subsystems."

See also

• Arrow of time
• Big Bang
• Big Bounce
• Big Crunch
• Big Rip
• Chronology of the universe
• Cyclic model
• Entropy (arrow of time)
• Fluctuation theorem
• Graphical timeline from Big Bang to Heat Death
• Heat death paradox
• The Last Question
• Terasecond and longer

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