|American chemical mineralogist Norman Dolloff, in his Heat Death and the Phoenix: Entropy, Order, and the Future of Man (1975), digresses on the thermal word laced notions of birth (phoenix myth) and death (heat death), in respect to the future of humankind, in particular how the laws of thermodynamics applied to the humanities may “enable man to organize his future.” |
“The cosmological prediction of entropic ‘heat death’ of the universe [occurs when] all available physical energy if used up, and all pockets of negentropic life will have disappeared forever.”
An early view of heat death was expressed in a March 21st 1869 letter from Friedrich Engels to Karl Marx: 
“In Germany the conversion of the natural forces, for instance, heat into mechanical energy, etc., has given rise to a very absurd theory—that the world is becoming steadily colder … and that, in the end, a moment will come when all life will be impossible. I am simply waiting for the moment when the clerics seize upon this theory.”
Said another way, heat death expresses the view that due to the maximization of entropy, and that all movement will stop, or reach equilibrium.  In the years to follow, people began to wonder how this "dissipation and death" postulate might related to human life. 
The idea of heat death stems from the second law of thermodynamics, which states that entropy to increase in an isolated system. If the universe lasts for a sufficient time, it will asymptotically 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 in time due to the second law.
|Irish physicist William Thomson, central promoter of the heat death theory.|
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.  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 Rankine and Helmholtz. The three of them were said to have exchanged ideas on this subject. 
Chinese-born American economist Ching-Yao Hsieh and American economist Meng-Hua Ye claim that Helmholtz predicted the heat death of the universe in 1854, thought no source is given. 
In 1862, Thomson published the article “On the age of the sun’s heat” 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 motion, and exhaustion of potential energy through the material universe while clarifying his view of the consequences for the universe as a whole. The key paragraph is: 
“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.”
|French astronomer Camille Flammarion’s 1893 depiction of heat death.|
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). 
In 1867, Rudolf Clausius, in his “On the Second Fundamental Theorem of the Mechanical Theory of Heat” lecture, introduced his heat death supposition as follows: 
"When two transformations are equal in magnitude but of opposite signs, we agreed above to say that they compensate each other. Accordingly we may enunciate the following theorem in reference to all the three kinds of transformations :—Negative transformations can take place only wlien they are compensated, but positive transformations can occur even if uncompensated; or, shorter still, Uncompensated transformations can never be anything but positive.
This peculiar relation is met with in every change that occurs in nature; for the case of an alteration being completely reversible, so that the sum of all the transformations involved in it is exactly zero, is merely the limiting case of an infinite number of possible cases, just as zero itself is the lower limit of all positive magnitudes. When we consider the universe, keeping this relation in mind, we arrive at a very remarkable conclusion.
One hears it often said that in this world everything is a circuit. While in one place and at one time changes take, place in one particular direction, in another place and at another time changes go on in the opposite direction; so that the same conditions constantly recur, and in the long run the state of the world remains unchanged. Consequently, it is said, the world may go on in the same way for ever.
When the first fundamental theorem of the mechanical theory of heat was established, it may probably have been regarded as an important confirmation of this view. Hitherto, when discussing this theorem, we have spoken only of heat and ergon; but it must be observed that we may regard the word "heat" as also including light; and the conception of "ergon" is very much more comprehensive still. Chemical action, the effects of electrical and magnetic forces, the production and cessation of motion, whether it be the progressive, rotatory, or vibratory motion of ponderable masses, or whether it be the motion of electricity, may all, so far as they are here considered, be represented as ergon. We are consequently dealing with a theorem that applies to all natural phenomena.
Helmholtz, who at once recognized this general significance of the theorem, and established it clearly and convincingly in his beautiful essay on this subject by applying the theorem to the various branches of physics, "ave to the theorem, when thus extended as widely as possible, ,he name of the Theorem of the Conservation of Force, for which it would perhaps be a little better still to say the Theorem of the Conservation of Energy.
When the object is to make it express a general fundamental law of the universe, this theorem may be put into some such form as the following:—One form of Energy can be transformed into another form of Energy, but the quantity of energy is thereby never diminished; on the contrary, the total amount of Energy existing in the universe remains just as constant as the total amount of Matter in the universe.
Notwithstanding that the truth of this theorem is beyond a doubt, and that it expresses the unchangeablencss of the universe in a certain very important respect, we should yet be going too far were we to assume that it affords a confirmation of the view according to which the whole condition of the universe is represented as unchangeable, and all involved in never-ending cycles. The second fundamental theorem of the mechanical theory of heat contradicts this view most distinctly.
As was said above, the common rule holds good for all the endlessly manifold changes which go on in the world, that transformations in opposite directions do not necessarily occur in equal numbers, but that the difference can only be on one determinate side, namely, so that the positive transformations preponderate over the negative. Hence it follows that the condition of the universe must gradually change more and more in a certain particular direction.
The ergon which the forces of nature are capable of performing, and which is contained in the existing motions of the bodies which make up the system of the universe, will be gradually converted more and more into heat. The heat, inasmuch as it always tends to pass from hotter to colder bodies, and so to equalize existing differences of temperature, will gradually acquire a more and more uniform distribution, and a certain equilibrium will be attained even between the radiant beat existing in the aether and the heat existing in material bodies. Lastly, in relation to their molecular arrangement, material bodies will get nearer to a certain condition in which, regard being had to the existing temperature, the total disgregation is the greatest possible.
I have endeavoured to express the whole of this process by means of one simple theorem, whereby the condition towards which the universe is gradually approaching is distinctly characterized. I have formed a magnitude which expresses the same thing in relation to transformations that energy does in relation to heat and ergon—that is, a magnitude which represents the sum of all the transformations which must have taken place in order to bring any body or system of bodies into its present condition. I have called this magnitude 'entropy'. Now in all cases in which the positive transformations exceed the negative an increase of entropy occurs. Hence we must conclude that in all the phenomena of nature the total entropy must be ever on the increase and can never decrease; and we thus get as a short expression for the process of transformation which is everywhere unceasingly going on the following theorem :— The entropy of the universe tends towards a maximum.
The more the universe approaches this limiting condition in which the entropy is a maximum, the more do the occasions of further changes diminish; and supposing this condition to be at last completely attained, no further change could evermore take place, and the universe would be in a state of unchanging death.
Albeit the present condition of the universe is still very far removed from this limiting condition, and the approach to it is so slow that all such periods as we speak of as historical are but a very short span in comparison with the immeasurable periods that the universe requires for comparatively very slight modifications, it yet remains an important result that a law of nature should have been discovered which allows us to conclude with certainty that everything in the universe does not occur in cycles, but that it changes its condition continually in a certain direction, and thus tends towards a limiting condition."
Thermodynamics historian Helge Kragh states that the "unchanging death" passage is representative of the heat death coining.  Another reference states that Clausius coined the term heat death in 1865.  The original German word for ‘heat death’ is ‘Wärmetod’. 
The following are related quotes:
“The tendency of heat is towards equalisation; heat is par excellence the communist of our universe, and it will no doubt ultimately bring the system to an end.”— Balfour Stewart and Peter Tait (1875) 
|A thermodynamics humor version of heat death (Ѻ), as the time when the entropy of the universe reaches a maximum.|
1. Daintith, John. (2005). Oxford Dictionary of Science. Oxford: Oxford University Press.
2. Thomson, William. (1951). “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]
3. Thomson, William (1952). “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.]
4. Smith, Crosbie & Wise, Matthew Norton. (1989). Energy and Empire: A Biographical Study of Lord Kelvin. (pg. 500). Cambridge University Press.
5. Thomson, William. (1862). “On the age of the sun’s heat”, Macmillan’s Mag., 5, 288-93; PL, 1, 394-68.
6. Physics Timeline (Helmholtz and Heat Death, 1854).
7. Ball, Philip. (2004). Critical Mass - How One Things Leads to Another, (pgs. 36-39, Quote: "the theory soon leads to discussions verging on the metaphysical"). New York: Farrar, Straus and Giroux.
8. Byrne, John, Toly, Noah, and Glover, Leigh. (2006). Transforming Power: Energy, Environment, and Society in Conflict (pg. 39). Transaction Publishers.
9. (a) Arrhenius, Svante. (1909). Worlds in the Making: the Evolution of the Universe (warmetod, pg. 193). Harper.
(b) Corning, Peter. (2005). Holistic Darwinism: Synergy, Cybernetics, and the Bioeconomics of Evolution (warmetod, pg. 313). University of Chicago Press.
10. (a) Kragh, Helge. (2007). Conceptions of Cosmos: from Myths to Accelerating Universe (2.4.1: heat death, pgs. 101-02). Oxford University Press.
(b) Clausius, Rudolf. (1868). “On the Second Fundamental Theorem on the Mechanical Theory of Heat”, Philosophical Magazine, 35:405-19, quote pg. 405.
11. Bertola, F. and Curi, Umberto. (1993). The Anthropic Principle (Clausius coined ‘heat death’ in 1865, pg. 69). Cambridge University Press.
12. De Quincey, Christian. (2002). Radical Nature: Rediscovering the Soul of Matter (pg. 296). Invisible Cities Press.
13. Hsieh, Ching-Yao, and Ye, Meng-Hua. (1991). Economics, Philosophy, and Physics (pg. xxvii). M.E. Sharpe.
14. Stewart, Balfour and Tait, Peter G. (1875). The Unseen Universe: or Physical Speculations on a Future State (§114). Macmillan.
15. Dolloff, Norman H. (1975). Heat Death and the Phoenix: Entropy, Order, and the Future of Man (abs) (free energy, 27+ pgs). Exposition Press.
16. Clausius, Rudolf. (1867). “On the Second Fundamental Theorem of the Mechanical Theory of Heat” (quote, pg. 419), A Lecture Delivered Before the 41st Meeting of the German Scientific Association, at Frankfort on the Main, Sep 23; in: Philosophical Magazine, 4(35):405-419, 1868.
● Heat death of the universe – Wikipedia.