# Heat death of the universe

For the album by Off Minor, see The Heat Death of the Universe.

The heat death of the universe is a historically suggested 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 consume energy (including computation and life). 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). 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.

In a more recent view than Kelvin's, it has been recognized by a respected authority on thermodynamics, Max Planck, that the phrase 'entropy of the universe' has no meaning because it admits of no accurate definition.[1][2] Kelvin's speculation falls with this recognition.

## Origins of the idea

The idea of heat death stems from the second law of thermodynamics, which states that entropy tends to increase in an isolated system. If the universe lasts for a sufficient time, it will asymptotically approach a state where all energy is evenly distributed. In other words, in nature there is a tendency to the dissipation (energy loss) of mechanical energy (motion); hence, by extrapolation, there exists the view that the mechanical movement of the universe will run down, as work is converted to heat, in time because of the second law. The idea of heat death was first proposed in loose terms beginning 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). Thomson’s views were then elaborated on more definitively over the next decade by Hermann von Helmholtz and William Rankine.

### 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 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."[3]

Lord Kelvin originated the idea of universal heat death in 1852.

In 1852, Thomson published his "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.[4] 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.[5] 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.[6]

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).[5][7]

## Current status

Inflationary cosmology suggests that in the early universe, before cosmic inflation, energy was uniformly distributed,[8] and the universe was thus in a state superficially similar to heat death. However, these two states are actually very different: in the early universe, gravity was a very important force, and in a gravitational system, if energy is uniformly distributed, entropy is quite low, compared to a state in which most matter has collapsed into black holes. Thus, such a state is not in thermodynamic equilibrium, as it is thermodynamically unstable.[9][10]

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 also expected to occur,[11] with the universe cooling to approach absolute zero temperature and approaching a state of maximal entropy over a very long time period. There is dispute over whether or not an expanding universe can approach maximal entropy; it has been proposed that in an expanding universe, the value of maximum entropy increases faster than the universe gains entropy, causing the universe to move progressively further away from heat death.[citation needed]

There is much doubt about the definition of the entropy of the universe. In a view more recent than Kelvin's, it has been recognized by a respected authority on thermodynamics, Max Planck, that the phrase 'entropy of the universe' has no meaning because it admits of no accurate definition.[1][2] Kelvin's speculation falls with this recognition. 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."[12] 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."[13] 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."[14] In the opinion of Čápek and Sheehan, "no known formulation [of entropy] applies to all possible thermodynamic regimes."[15]

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.[16] 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."[17] In other words, this writer is saying that when gravity is taken into account (which Kelvin did not), a prediction of heat death is not justified.

## Time frame for heat death

From the Big Bang through the present day and well into the future, matter and dark matter in the universe are thought to be concentrated in stars, galaxies, and galaxy clusters. Therefore, the universe is not in thermodynamic equilibrium and objects can do physical work.[18], §VID. The decay time for a supermassive black hole of roughly 1 galaxy-mass (1011 solar masses) due to Hawking radiation is on the order of 10100 years,[19] 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.[18], §VIA. 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.[18], §VE. It is also possible that entropy production will cease and the universe will achieve heat death.[18], §VID. Possibly another universe could be created by random quantum fluctuations or quantum tunneling in roughly $10^{10^{56}}$ years.[20] Over an infinite time there would be a spontaneous entropy decrease by Poincaré recurrence theorem, thermal fluctuations[21][22] and Fluctuation theorem.[23][24]

## References

1. ^ a b
2. ^ a b Uffink, J. (2003). Irreversibility and the Second Law of Thermodynamics, Chapter 7 of Entropy, p. 129 of Greven, A., Keller, G., Warnecke (editors) (2003), Entropy, Princeton University Press, Princeton NJ, ISBN 0-691-11338-6. Uffink asserts the authority of Planck's text.
3. ^ Thomson, William. (1851). "On the Dynamical Theory of Heat, with numerical results deduced from Mr Joule’s equivalent of a Thermal Unit, and M. Regnault’s Observations on Steam." Excerpts. [§§1–14 & §§99–100], Transactions of the Royal Society of Edinburgh, March, 1851; and Philosophical Magazine IV. 1852. [from Mathematical and Physical Papers, vol. i, art. XLVIII, pp. 174]
4. ^ Thomson, William (1852). "On a Universal Tendency in Nature to the Dissipation of Mechanical Energy" Proceedings of the Royal Society of Edinburgh for April 19, 1852, also Philosophical Magazine, Oct. 1852. [This version from Mathematical and Physical Papers, vol. i, art. 59, pp. 511.]
5. ^ a b Smith, Crosbie & Wise, Matthew Norton. (1989). Energy and Empire: A Biographical Study of Lord Kelvin. (pg. 500). Cambridge University Press.
6. ^ Thomson, William. (1862). "On the age of the sun’s heat", Macmillan’s Mag., 5, 288–93; PL, 1, 394–68.
7. ^ Physics Timeline (Helmholtz and Heat Death, 1854)
8. ^ Andrew R Liddle; Andrew R Liddle (1999). "An introduction to cosmological inflation". arXiv:astro-ph/9901124 [astro-ph].
9. ^ Hawking, S.; S. W. Hawking (1976). "Black holes and thermodynamics". Physical Review D 13 (2): 191. Bibcode:1976PhRvD..13..191H. doi:10.1103/PhysRevD.13.191.
10. ^ S. W. Hawking and Don N. Page. "Thermodynamics of black holes in anti-de Sitter space". Comm. Math. Phys. 87, no. 4 (1982), 577–588. Retrieved 2006-09-09.
11. ^ Plait, Philip Death From the Skies!, Viking Penguin, NY, ISBN 978-0-670-01997-7, p. 259
12. ^ Grandy, W.T. (Jr) (2008). Entropy and the Time Evolution of Macroscopic Systems, Oxford University Press, Oxford UK, ISBN 978-0-19-954617-6, p. 151.
13. ^ Landsberg, P.T. (1961). Thermodynamics, with Quantum Statistical Illustrations, Wiley, New York, p. 391.
14. ^ Lieb, E.H., Yngvason, J. (2003). The entropy of classical thermodynamics, Chapter 8 of Greven, A., Keller, G., Warnecke (editors) (2003). Entropy, Princeton University Press, Princeton NJ, ISBN 0-691-11338-6, page 190.
15. ^ Čápek, V., Sheehan, D.P. (2005). Challenges to the Second Law of Thermodynamics: Theory and Experiment, Springer, Dordrecht, ISBN 1-4020-3015-0, 26.
16. ^ Egan; Chas A. Egan and Charles H. Lineweaver (2009). "A Larger Estimate of the Entropy of the Universe". arXiv:0909.3983 [astro-ph.CO].
17. ^ Smolin, L. (2014). Time, laws, and future of cosmology, Physics Today, 67: 38–43, page 42.
18. ^ a b c d Fred C. Adams and Gregory Laughlin (1997). "A dying universe: the long-term fate and evolution of astrophysical objects". Reviews of Modern Physics 69 (2): 337–372. arXiv:astro-ph/9701131. Bibcode:1997RvMP...69..337A. doi:10.1103/RevModPhys.69.337..
19. ^ Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole, Don N. Page, Physical Review D 13 (1976), pp. 198–206. doi:10.1103/PhysRevD.13.198. See in particular equation (27).
20. ^ Carroll, Sean M. and Chen, Jennifer (2004). "Spontaneous Inflation and Origin of the Arrow of Time". arXiv:hep-th/0410270.
21. ^ http://arxiv.org/pdf/astro-ph/0302131.pdf?origin=publication_detail
22. ^ http://arxiv.org/abs/1205.1046
23. ^ http://www.researchgate.net/publication/2215242_Spontaneous_entropy_decrease_and_its_statistical_formula
24. ^ http://iopscience.iop.org/1475-7516/2007/01/022