# Heat death of the universe

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The **heat death of the universe**, also known as the **Big Chill** or **Big Freeze**,^{[1]} is a conjecture on the ultimate fate of the universe, which suggests the universe would evolve to a state of no thermodynamic free energy and would therefore be unable to 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 consistent with current data), the universe will continue expanding forever, and a heat death is expected to occur,^{[2]} 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 Lord 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.

## ConceptEdit

The concept of the heat death of the universe is based on the observation that the gravitational potential energy of the universe, also known as rest mass that is stored mostly in baryons, self‑gravitationally shrinks and heats up to ever higher temperatures. Consequently, the ever‑smaller and ever‑hotter baryons "evaporate", with an exponential acceleration, into the seemingly expanding ambient space as photons, so that eventually the universe will consist of zero‑frequency photons:

If the rest mass decreases by Δ

m_{0}, the kinetic energyE=c^{2}Δm_{0}is produced. The same thing is true if we replace production of kinetic energyEby production of radiant energyE. Continuing this line of argument, one can envisage the possibility that the whole rest massmof a body could be converted into energy. Then the energyE=m_{0}c^{2}would be produced and the whole rest mass of the body would disappear.

- —International Encyclopedia of Unified Science Vol. 1, nos. 6–10, University of Chicago Press, 1955, p. 460

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. On the Age of the Sun’s Heat
Macmillan's Magazine, 5 March 1862, pp. 388–93

The exponential acceleration of baryons' evaporation has been described by Arthur Eddington:

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.

- —Eddington, Arthur. The Expanding Universe CUP, 1933, pp. 90–92

After the evaporation of all baryons, the resultant bath of zero‑frequency photons, indistinguishable from empty space, will condense into new protons, each miles across, which will undergo another 13.8‑billion‑year‑long exponentially accelerating shrinkage and evaporation. And so *ad infinitum*:

According to the standard view, dark energy will lead the universe into an eternal accelerating expansion. Every bit of matter will eventually lose contact with every other bit. "It all just seemed unbelievably boring to me," Penrose says. Then he found something interesting within it:

at the very end of the universe, the only remaining particles will be massless. That means everything that exists will travel at the speed of light, making the flow of time meaningless.After a few mathematical manipulations of infinity, out popped a never‑ending universe, where new big bangs are the inevitable result of a universe's demise. In Penrose's theory, one cosmos leads to another. "I used to call it a crazy scheme, but I'm starting to believe it now," he says.

- —Brooks, Michael. Roger Penrose: Non-stop cosmos, non-stop career
New Scientist, 10 March 2010

## Origins of the ideaEdit

The idea of heat death stems from the second law of thermodynamics, of which one version states that entropy tends to increase in an isolated system. From this, the hypothesis implies that if the universe lasts for a sufficient time, it will asymptotically approach a state where all energy is evenly distributed. In other words, according to this hypothesis, there is a tendency in nature to the dissipation (energy transformation) of mechanical energy (motion) into thermal energy; hence, by extrapolation, there exists the view that, in time, the mechanical movement of the universe will run down as work is converted to heat because of the second law.

The conjecture that all bodies in the universe cool off, eventually becoming too cold to support life, seems to have been first put forward by the French astronomer Jean Sylvain Bailly in 1777 in his writings on the history of astronomy and in the ensuing correspondence with Voltaire. In Bailly's view, all planets have an internal heat and are now at some particular stage of cooling. Jupiter, for instance, is still too hot for life to arise there for thousands of years, while the Moon is already too cold. The final state, in this view, is described as one of "equilibrium" in which all motion ceases.^{[3]}

The idea of heat death as a consequence of the laws of thermodynamics, however, was first proposed in loose terms beginning in 1851 by Lord Kelvin (William Thomson), who theorized further on the mechanical energy loss views of Sadi Carnot (1824), James Joule (1843) and Rudolf Clausius (1850). Thomson's views were then elaborated over the next decade by Hermann von Helmholtz and William Rankine.^{[citation needed]}

### HistoryEdit

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, Lord Kelvin outlined the view, as based on recent experiments on the dynamical theory of heat: "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."^{[4]}

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 naturally tend to dissipate or run down.^{[5]} 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.^{[6]} 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. 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.

^{[7]}

In the years to follow both Thomson's 1852 and the 1862 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).^{[6]}^{[8]}^{[unreliable source?]}

## Current statusEdit

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, either a heat death or a Big Rip is expected to eventually occur.^{[2]} 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 in which no further work is possible.^{[9]}

If a Big Rip does not happen long before that, the "heat death" situation could be avoided if there is a method or mechanism to regenerate hydrogen atoms from radiation, dark matter, dark energy, zero-point energy, or other sources. If so, it is at least possible that star formation and heat transfer can continue, avoiding a gradual running down of the universe due to the conversion of matter into energy and heavier elements in stellar processes, and the absorption of matter by black holes and their subsequent evaporation as Hawking radiation.^{[10]}^{[11]}

## Time frame for heat deathEdit

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 do so well into the future. Therefore, the universe is not in thermodynamic equilibrium, and objects can do physical work.^{[12]}^{, §VID.} The decay time for a supermassive black hole of roughly 1 galaxy mass (10^{11} solar masses) due to Hawking radiation is on the order of 10^{100} years,^{[13]} so entropy can be produced until at least that time. Some large black holes in the universe are predicted to continue to grow up to perhaps 10^{14} `M`_{☉} during the collapse of superclusters of galaxies. Even these would evaporate over a timescale of up to 10^{106} years.^{[14]} 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.^{[12]}^{§VIA} With only very diffuse matter remaining, activity in the universe will have tailed off dramatically, with extremely low energy levels and extremely long timescales. 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.^{[12]}^{, §VE.} It is also possible that entropy production will cease and the universe will reach heat death.^{[12]}^{, §VID.} Another universe could possibly be created by random quantum fluctuations or quantum tunneling in roughly years.^{[15]} Over vast periods of time, a spontaneous entropy *decrease* would eventually occur via the Poincaré recurrence theorem,^{[16]} thermal fluctuations,^{[17]}^{[18]}^{[19]} and fluctuation theorem.^{[20]}^{[21]} Such a scenario, however, has been described as "highly speculative, probably wrong, [and] completely untestable".^{[22]} Sean M. Carroll, originally an advocate of this idea, no longer supports it.^{[23]}^{[24]}

## ControversiesEdit

Max Planck wrote that the phrase "entropy of the universe" has no meaning because it admits of no accurate definition.^{[25]}^{[26]} More recently, Walter 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."^{[27]} According to Tisza: "If an isolated system is not in equilibrium, we cannot associate an entropy with it."^{[28]} Buchdahl writes of "the entirely unjustifiable assumption that the universe can be treated as a closed thermodynamic system".^{[29]} According to Gallavotti: "... there is no universally accepted notion of entropy for systems out of equilibrium, even when in a stationary state."^{[30]} 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."^{[31]} 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."^{[32]}

A 2010 analysis of entropy states, "The entropy of a general gravitational field is still not known", and, "gravitational entropy is difficult to quantify". The analysis considers several possible assumptions that would be needed for estimates and suggests that the observable universe has more entropy than previously thought. This is because the analysis concludes that supermassive black holes are the largest contributor.^{[33]} Lee Smolin 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."^{[34]}
This point of view is also supported by the fact of a recent experimental discovery of a stable non-equilibrium steady state in a relatively simple closed system. It should be expected that an isolated system fragmented into subsystems does not necessarily come to thermodynamic equilibrium and remain in non-equilibrium steady state. Entropy will be transmitted from one subsystem to another, but its production will be zero, which does not contradict the second law of thermodynamics.^{[35]}^{[36]}

## See alsoEdit

- 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*- Timeline of the far future
- Orders of magnitude (time)
- Thermodynamic temperature

## ReferencesEdit

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