B. Lukács


President of the Matter Evolution Subcommittee of the Geonomy Scientific Committee of HAS


CRIP RMKI, H-1525 Bp. 114, Pf. 49, Budapest, Hungary



            S. M. Stirling is writing books in Alternate History. Besides the obvious evolutionary connections, these books suggest lots of interesting scientific or scholarly problems, some discussed in the books, some not. In the “Emberverse” stories mighty aliens perturb terrestrial physics stopping detonations and flow of electricity since March 17, 1998, 18h30m PST. We could not do this, so we do not know how the aliens did it. The survivors discuss it, but in a rather non-physicist way. Here I am going to discuss the problem from the viewpoint of Thermodynamics.



            S. M. Stirling is producing a big variety of Alternative History sci-fi’s. Alternative History is a subclass of sci-fi’s, where the fantasy does not enjoy its unlimited freedom. In an ideal AH story only one event has other outcome than on our timeline (that is the PoD, Point of Divergence), especially an event which "might have happened as well otherwise", by other words, where even now we do not know if the particular outcome was necessary or not. (Here I omit philosophical discussions of Free Will, determinism/indeterminism, the Everett Theory of Quantum Mechanical Measurement and such, for simplicity.) So at PoD one event has another outcome, and then the author continues the story, with as strict "causality" as possible. Of course the PoD acts then as an initial condition different than in Our TimeLine (OTL). Then the author elaborates this Alternative History.

            Now, we do not yet know if such concurrent timelines can be realised "synchronously", or not. (Against the a priori impossibility of the alternative see Everett's famous paper [1].) But even this were impossible, the elaboration is edifying. Anyway, if one believes in Free Will (this is religion-dependent, of course), one should think over the alternatives before any important decision.

            The machinery can be demonstrated by means of, e.g., Poul Anderson's works. In Eutopia [2] a modern (c. 1970 AD) Greek social researcher from a timeline where Alexander III of Macedon did not drink himself exactly into death but after some time recovered, so Aristotle did not have to leave the Lyceum  in 322 AD, can switch timelines, and explores one where Alexander did die prematurely, but the Tours-Poitiers battle in 732 AD had an outcome opposite than in OTL. So the Frankish Kingdom became weaker, the Pippin-Charlemagne line could not substitute the Merovings, so in the next 200 years Dane Vikings & Magyars destroyed the Western Christian civilisation. In 1970 AD Danes can be found in Canada & Minnesota (Anderson's state) and Magyars along the Mississippi (Dakoty). In another mininovel [3] Sulmanu-Assaridu King of Assyria took Jerusalem in 701 BC (this was the probable outcome; we still do not know what happened, but the Holy Bible is also not too definite). Then no Judaism from VII c. BC upward, so no Christianism either; the Roman Empire breaks down in a somewhat less dramatic way, in 1976 AD the Visigothic Kingdom is the strongest Mediterranean power, Mithraism is the strongest religion on Southwest, Mazdaism in Southeast, and the North is pagan. And again: Danes in Canada & Minnesota and Magyars in the Mississippi Basin.

            S. M. Stirling works in the AH scheme. In one sequence (Lords of Creation [4], [5]) the PoD was 200 My in the past; a superhuman civilisation terraformed Venus & Mars, and from time to time they imported new animals & plants to the other two planets. Terrestrial history was practically not influenced until 1947 AD, when astronomers detected the habitable planetary surfaces. Therefore Cold War went to space. The Draka sequence of Stirling puts the PoD to somewhere at the second half of the XVIIIth century, Northern American loyalists go to South Africa, so the XXth century will be very, very different. (But this sequence is par excellence Military SF, so I ignore it completely.)

            Now, Stirling & Flint invented a somewhat different new AH scenario. (I think Stirling was somewhat earlier, but Flint in the 1632 Universe of Assiti Shards has a big net of collaboration, so novels are published rather fast.)

            The idea is "simple". A tremendously superhuman ET civilisation sends back a negligible part of our contemporary Earth into the past, and replaces the surface with the past one. In Flint's 1632 [6] a West Virginian small miner town of 2000 is sent back to Thuringy in 1631, the heyday of the Thirty Year War.

            Stirling's somewhat similar scheme produced so far 6 full novels, 1 novelette, a 7th novel is just being published, and 1 in preparation [7-15]. In [7-10] Something sends back the Island of Nantucket and its immediate maritime neighbourhood from 1998 AD to 1250 BC. The Nantucketers sometimes discuss what may have happened, and they agree that most probably the 1250 BC Nantucket emerged in 1998 AD, but, of course, they cannot check. Then [11] is the opposite viewpoint: post-Change USA. Some Superhuman agency slightly changed some Physical Laws on the 1998 surface of Earth, so that the Boyle-Mariotte Gas Law changes, so gasoline engines do not work, gunpowder merrily burns but does not detonate, steam engines can work only with negligible efficiency and there is no electric current (I do not yet understand the relation of the last change to the previous ones). High energy 1998 civilisation breaks down and the overwhelming majority of Humanity dies out; but at some centers good organisers found a post-Change civilisation, a viable hybrid of XXth century and High Middle Ages. And then [14] starts to sew together [7-10] with [11-13], and with more Realities as well. I conjecture that in a few years Stirling will write something establishing a link between the Lords of Creation and the Nantucket anomaly.

            While this opus is not yet comparable in size and details with that of Honoré de Balzac, it may be later; and while Balzac had to know only his present society and its immediate past, Stirling is confronted with scientific problems, and with a number of different societies. True, the scientific problems are not direct. Earthpeople do not understand the Lords of Creation; not even the bioscience of Martian hominids. But Stirling should; or at least has to make the impression he knows more about than us.

            So far he generally fulfils the expectations. But the opus is a challenge for somebody (I mean myself) who is the President of a Matter Economy Subcommittee. Evolution of sciences, evolution of languages, evolution of hominids...

            I am going to make a series of comments of that opus. That will not be criticism. Nobody is interested if I like or dislike a book. Rather I am going to discuss different items in the books from the viewpoint of the actual science (or, sometimes, scholarship).

            Sometimes this is really a challenge. E.g. Lords of Creation definitely use a physics unknown for us. And our present physics is not the Physics. For 2000 years it was not only elementary experience but also Fundamental Theory that there is no Motion (at least, except for transients,) without Force. People generally believe that Aristotle was stupid and the later generations did not dare innovate; but Aristotle did know that his theory was not yet complete. See his own words about the problem of ballistics (spears and arrows) [16]. In Chap. 32 of Mechanics he writes: "Why is it that an object which is thrown eventually comes to a standstill? Does it stop when the force which started it fails, or because the object is drawn in a contrary direction, or is it due to its downward tendency, which is stronger than the force which threw it? Or is it absurd to discuss such questions, while the principle escapes us?" (Italics are mine.) The paragraph is clear enough even it contains only questions. The Stagirite did know that ballistics was at best very difficult to describe even in his theory; and he was not able to do. Still, missiles flew; and later somebody would improve even his description.

            Before Einstein's success not only everybody in physics was convinced that Flow of Time was independent of spatial motions; everybody believed that even a doubt would be meaningless. Special Relativity appeared a mere 103 years. Similarly, until the formulation of Quantum Mechanics (more or less 1926) physicists were convinced that any object has its sharp momentum and position, although maybe we do not know them; and similarly that one object cannot be simultaneously here and there. It seemed defetism to question the first statement and unscientific magic the second. That was 82 years ago.

            Our present science will be so primitive and untrue for the XXVth century as the Aristotelian physics for us. Still, Aristotle was a true scientist (while Platon, Marcion, Plotinos and Melanchton were not), as a true physicist as  e.g. Galileo, Newton and Einstein. Our present physics will not be substituted by a free choice of personal theories (Aquarius or not Aquarius) but by a still unknown new theory explaining what the previous theory did and some further ones as well. And then, after a time the next theory will be disproven as well...

            Stirling's books show alternate realities. We know only one of them; but there may be others. But are the stories consistent at least with our present knowledge plus the assumption that Alternate Realities can exist? This is a nontrivial but very interesting question.

            Here we are going to discuss the thermodynamic problems arising in Stirling's Emperverse sequel.



            Emberverse Scenario is one half of a timeline; but for all practical purposes we can call a timeline the Ember TimeLine or ETL, because on one of who knows how many alternative TL's "the Fire Dies" on Earth in March 1998 and "only Embers remain".

            Well, this is metaphoric speech and exaggeration. Fires continue to burn quite well after the Change, but intense fires are slightly less intense. But this means that gunpowder only burns, does not detonate. And internal combustion engines do not work either. This two facts are observed seconds after the Change. Later it turns out that the efficiency of steam engines decline too.

            Electricity stops at the Change as well. Not only the electric networks stop; that might be a consequence of the stopping of power stations. Instead, electric wristwatches stop immediately too.

            Something drastic happened; about physical laws. The question is not if that is possible; perhaps the whole thing was made by Alien Space Bats, superhuman mighty aliens. Also, the important question is not: how? The technology of the Alien Space Bats is so above ours that we cannot answer the how until a new civilisation is not built up and in it lots of research is not made. The reasonable question is: which laws have changed. If one can answer this, one can start to build up optimally the new civilisation.

            In the Embervere sequel people sometimes guess that the laws of Thermodynamics have changed. I do not believe this. An Earth with a new Thermodynamics would be much more exotic than the Emberverse sequel reports it. But this needs some exposition and that will be done here.

            The Emberverse sequel (so far Refs. [11]-[15]) is one half of the story of one Alternate TL. The Change, made by the unknown aliens, was centered on the Island of Nantucket. No doubt, later we shall get additional information and then a more coherent pattern may emerge; but even now we do know that on Nantucket something additional happened as well. During the Change the "present" Nantucket got back to the spring of 1250 BC, and the "then" Nantucket substituted it (see [14]). So the Nantucket sequel [7]-[10] is theoretically the same TL, but because of the acausal effect it is practically disjoint. Still, we can learn that the changes of physical laws are exclusively after March 1998; on the pastplanted gunpowder and electricity do work.



            The Change, which was global, is described in details in [7] (Nantucket), in [11] (Oregon) and, briefly, in [12] (London). The effect was global and strange; in addition, the 1998 Nantucket Island + maritime neighbourhood had been commuted with the same island from 1250 BC (see [14]). In the present study I ignore the temporal anomaly. Surely strong electromagnetic processes were involved in the Change; see [7].

            It seems that the Change was not instantaneous. In Oregon broadcast listeners got the information that Something was happening in Nantucket just before the Change. Present information is insufficient to say more. But it seems that outside of Nantucket the Change was fast, a few seconds at most: some neural effects (e.g. a "light" seen also by the blind), and then electricity stopped, guns ceased to fire and combustion engines stopped too.

            Just then no research happened; there was simply a mass panic ind in months the overwhelming majority of urbanised population died out. (Without electricity and car engines city water supply and transport of goods stop immediately, natural gas supply soon &c.) However later the survivors have some possibilities to investigate the effects.

            The Change arrived at Oregon in 18h30m PST on 17th March, 1998. In Nantucket it started as an "electric storm" some minutes (at most) earlier; no electric storm was observed in London & Oregon. It seems that its effect is purely terrestrial; no data yet how high in the atmosphere. There are arguments that it was deliberately caused by very advanced aliens, or Alien Space Bats, henceforth ASB (for the argumentation see Chap. 9 of [11]). We (in OTL, getting information solely from the sequel(s)) cannot yet tell if the Agents of the Change who caused the Emberverse TimeLine (PoD March 17/18 1998) and the Nantucket Timeline (PoD the same but immediately transferred back to 1250 BC) are/were in any connection with the Lords of Creation ([4], [5]) who acted first 200 My ago, but who monitor the Solar System since then; maybe we shall get information in the future.

            1998 AD civilisation has been impossible to continue (no electricity, no engines), but lots of information remained, mainly in books. Some top administration and its structure survived in the United Kingdom. Substantial part of the society survived in Tasmania and the Southern Island of New Zealand. In Oregon a whole university (OSU in Corvallis) survived, with the faculty structure; we do not yet know about the universities in Tasmania & New Zealand. In England at least one university was refounded soon. Still, we have not got information about the university researches on the Change. Most research reports come to us from the Bearkiller community (Oregon), where the engineer father-in-law of the Chief Lord Bear ( Mike Havel, originally airplane pilot) performs methodical experiments. However keep in mind that he is an engineer, not physicist.

            Experiments of Larsson and the events mentioned in the Emberverse sequel have told us so far the following stationary changes:




Gunpowder does not detonate anymore, only burns fast

[11] Ch. 2 & passim

Electricity does not work, down to transistor radios; however neural systems are uneffected

[11] Ch. 2 & passim

Internal combustion engines do not work

[11] Ch. 2 & passim

Steam engines in principle work, but the efficiency is negligible

[11] Ch. 28

Stirling engines does not work in the direction of heat→motion. However they can be used slowly backwards, so refrigeration is possible if turning is yielded by horses or windmills

[12] Ch. 2

Combustion has become slower

[12] Ch. 2, [14], Ch. 5

Napalm &c. still burn fast enough

[11] Chs. 28 & 31

Nuclear chain reactions are somehow inhibited, but radiation still kills

[12] Ch. 8


            We can follow a substantial discussion of Ken Larsson, Scientific Advisor to Lord Bear and Lord Bear himself in [12], Ch. 2 where they concluded from experiments that on post-Change Earth

            The Gas Law has changed.

            There is some "glueing together" in gases.

            In a cylinder of a steam engine pressure p cannot go above a moderate limit, either T is increasing or V is decreasing.

            Still "concentrated heat" is possible, so foundries &c. work.

            The energy conservation is still valid, but the extra work goes into heat.

            Ken Larsson concludes that somehow Thermodynamics has changed ("It simply fucks parts of the laws of thermodynamics..."); in the next Chapter we discuss this possibility. But I tell the result already here: this solution is extremely improbable and surely reflects the engineers' picture about Thermodynamics. Namely, it is much more probable that "only" the equations of state of gases have changed.



            OTL Thermodynamics is mainly a theory/paradigm speaking about energy balances and probabilities. We have been collecting many empirical facts about that area in the last 2500 years (yes; our Thermodynamics continues to be Aristotelian for structure [17]), and now it is roughly as follows [18]-[21]:

            There are extensive parameters, whose minimal but sufficient set (finite) fully determine the equilibrium state of a thermodynamic system (apart from phase transitions when two or three different states may exist with the same extensives, but one is the stablest). You may think e.g. of a simple system of a single particle component without magnetism &c.; then the independent extensives are maybe {V,E,N}. For moderate gradients in the system you may switch to densities E/V and N/V and hope that the local state is still determined by the local densities (the principle of local equilibrium); in many cases this is true.

            Explanation: there is an energy distribution of maximal probability in the system. In or near to equilibrium it is probable that the internal state of the system is in the neighbourhood of the state of maximal probability. This state is determined by a finite set of macroscopic variables, as the total energy, the volume in which it is distributed, the number of particles on which it can be distributed &c.

            For large enough systems internal forces of short range ("surface forces) are negligible (a large container has "much more volume than surface"), so let us neglect them. Long-range interactions are mainly electromagnetism & gravitation. Electromagnetism can be roughly classified into electric force and magnetic force. Electric force is indeed of infinite range (or 1/r2 law), but the problem has negative feedback (in a neutral system fluctuations can produce positive and negative clusters, but the opposites attract each other, so this separation is transient). Not being magnetic monopoles (or, anyway, not being found), magnetism is formally not of infinite range. As for gravity, it is strong for really large systems as stars & galaxies, but the self-gravity of a steam engine is negligible. So we ignore volume forces.

            Comment: Thermodynamics of plasmas (with charged clusters) is possible but quite difficult. The behaviour of systems with internal magnetism was manageable up to now but surprises are not ruled out. Newtonian gravity is really a possibility of positive feedback, and this is the reason for e.g. star formation when the final configuration is more inhomogeneous than the initial one was (so no equilibration). In General Relativity Gravity is not an interaction at all but Geometry, and it is not yet completely settled how to handle it together with Thermodynamics.

            There is a thermodynamic potential, meaning that its extremum acts as a variational principle. So local functional dependences (as between pressure & energy & such) are determined from the functional form of the potential, for spontaneous processes the potential changes into a definite direction &c. For a simple system of independent extensives {V,E,N} this potential is maybe the entropy S, and then

              S = S(V,E,N)                                                                                                                         (3.1)

This S takes its maximum for equilibria in a closed system.

          Comment: this S must be in some connection with the distribution of the energy in the system, otherwise its functional form could not determine the particular functional forms amongst the quantities in the system. Indeed, Planck showed that for ideal gases

            lnS ~ kW                                                                                                  (3.2)

k being simply the Boltzmann constant and W the number of microstates belonging to the same macrostate; there are good arguments that the connection remains true for almost-ideal gases and it is used also for strongly non-ideal ones as well, for which our description is not yet two reliable, anyway. And then look: the spontaneous increase of S can be verbalised as: it is probable that a state is followed by another state even more probable.

            As told then earlier, the volume interactions are absent and the surface ones can be ignored for a large enough system. Now, consider a doubly large one in equilibrium. None will change if you separate it into two halves by a wall, either virtual or real. So the thermodynamic potential must be halved too, otherwise it would give changed forms of connections between half-energy, half-volume, half-number &c. By other and more unequivocal words, the potential is a homogeneous linear function of its extensive variables

              S = ∑S,RXR                                                                                                                           (3.3)

where XI's are the independent extensives, the comma means partial derivative, and the sum sign is left out henceforth according to the Einstein convention (i.e. that the same index in strict pairs, above and below, indicates summation). So entropy is an extensive too. The partial derivatives of the potential are called the canonically conjugate intensives, and are denoted by Y's, so

              YI = S,I                                                                                                                                  (3.4)

            Comment: being Y's the derivatives of the homogeneous linear potential with respect to extensives, the values of intensives are insensitive of the size of an equilibrium system.

            The change of the potential can of course be expressed via the changes of its all independent variables. So

              dS = S,RdXR = YRdXR                                                                                                           (3.5)

This is the differential form of the First Law.

            Explanation: For anybody but people really in Thermodynamics it is more natural to formulate the First Law for energy not for entropy. However when there is a single internal energy in the system then the two conventions are equivalent, and when ther are more than one internal energies in the system then only (3.5) is correct.

            But now from (3.3-5) it follows that

              XRdYR = 0                                                                                                                             (3.6)

This is called historically the Gibbs-Duhem relation, but it is a consequence of the above formulation.

            Comment: so there is no thermodynamics without (3.6). You might, on the other hand modify the First Law (3.5); but that may simply mean that you had forgot about some variables and now you are going to repair this. I am not discussing holy “conservation”; eq, (3.5) simply means that S can change only through its variables.

            Now, we are almost ready. In the usual axiomatic construction the 0th Law is the existence of the finite set of extensives and intensives, the First Law is (3.5), the Second Law is a consequence of the fact that S is a thermodynamic potential, so it fulfils some extremum principle, and the further Laws fix zeros or infinities of intensives. Generally only the Third Law, or Nernst's Law is explicitly formulated, establishing something about the absolute zero of temperature, or the thermodynamic behaviour of the system when approaching ground state, however for the fixing of convention the asymptotic behaviours in the infinities also need further Laws or Axioms. See e.g. [18], [22], [23].

            Explanation: if you do not understand a word of the last few sentences, you can remain happy. These sentences were a shortcut of several pages, which would not be interesting at all, except for cca. 1 of a million (estimation on Hungarian data).

            And now comes the last, hardly obvious, but very important point. The rank of the Pfaffian form of our Thermodynamics is 2.

            The exact, punctual and absolutely correct formulation would belong to Differential Geometry. I could reproduce it (after a half-day reading), but maybe it would be boring for you. However leaving off some details it goes as follows. Assume that you have already defined the reversible and irreversible parts of energy exchange, or defined somehow the natural or spontaneous or adiabatic processes or such. Then

              dE = dW + dQ                                                                                                                       (3.7)

where the strikethrough in the last term will get its explanation soon. Here dW is the reversible work (say, work of pressure) and dQ is the contribution of irreversible processes, generally called "heat transfer", or "noncompensated heat", although nobody ever has proven that only heat transfer can be irreversible.

            Now, the Pfaffian form is connected with dQ. But first observe that dQ is not unequivocally defined [21]. Namely, you may add some part of dW to dQ and still the new d'W and d'Q will remain reversible and irreversible, respectively. People generally do not discuss this problem and so let us believe now that this freedom is irrelevant for the rank of the Pfaffian.


              dQ = GR(XI)dXR                                                                                                                    (3.8)

being the set of the independent extensive variables complete, and also all the coefficients GI are functions of homogeneous zeroth order. Otherwise they depend on the details of, e.g., the intermolecular interactions. But if we know the function S(XI) and we know which change is reversible and which is not, then we know the G's.

            Now, let us introduce new variables Qi

              Qi = Qi(XK), 1≤i≤n≤N, 1≤K≤N                                                                                             (3.9)

Then eq. (3.8) takes the new form

              dQ = gr(Xk)dQr                                                                                                                      (3.10)

Different transformations result in different values of n (the length of summation). Let us take the one with minimal n. (If there are two transformations with the same n, we may take any of them.) And now dQ can be written as one of the possibilities


  dQ = dQ



  dQ = g(XI)dQ



  dQ = g(XI)dQ1 + dQ2


and so on. And K is the rank of the Pfaffian.

            Now, in the case of K=1 there is an extensive variable Q, the heat, so then dQ = dQ, the noncompensated heat is just the change of an extensive variable. In this case there would be irreversibilities in thermodynamics, but there would not be a temperature. This is not the OTL world, but not the ETL one either.

            For K=2 one gets dQ=TdS, and this is OTL physics.

            For K=3 Thermodynamics would be "more complicated" than ours. But before anybody would be happy, note that if K>2, perpetua mobilia of second type are possible [19]. One such perpetuum mobile works as follows. You have lots of water of the Pacific of, say, 70 F°. Now, you separate half and half of the volume, cool the first to 50 F° and heat the other to 90 F°. No change in total energy. But then you can drive a heat engine with the temperature difference! After some time you are back at the initial situation, but the heat engine performed some work!

            In OTL this does not work; it takes more energy to cool and heat than the work you get back afterwards, and the difference is just the "noncompensated heat". You may generalise the long experience for the impossibility into an Axiom that K≤2.  In contrast, in a K=3 world some really ingenious engineers could build perpetua mobilia even with energy conservation. (For the possible physics in the remote past of the Universe see [24]; but I do not argue for it, only state the possibility.) Now, the reports [11]-[15] do not suggest such a situation after Change, ergo K is still 2 in ETL. It seems that nothing mentioned in this Chapter changed in ETL on 17 March, 1998.



            The discussion so far was to demonstrate that, contrary to Ken Larsson's opinion [12] very probably the Change has not changed the Laws of Thermodynamics. OK, Ken Larsson is an engineer, not a physicist, so he did not formulate the statement as Callen, Landsberg or Martinás would have made it. However he did get some intuition, see again Chap. 2 of [12].

            At a point he tells: "...instead of producing work, the heat energy or the work put into mechanical compression gets locked into some weird form of potential energy". Even if this statement is somewhat indefinite (it is far not the same case if heat or mechanical compression goes into weird potential energy), we can formulate the nebulous hypothesis behind.

            Assume that you have two disjoint energies in thermodynamic sense, E1 and E2, in the system. Then

              S = S(V,E1,E2,N)                                                                                                                   (4.1)

For physical examples see e.g. [25] & [26]. This means two energy reservoires. Of course, only the sum has conservation or any other balance law.

            To explain this, let us take the example discussed in [25]: a LiF crystal in external magnetic field. The ions are near to the points of a cubic lattice, and oscillate around. This is the familiar thermal motion. However the spins of the nuclei of the ions can take up/down, so +/- positions relative to the external magnetic field.

            Now, the two ways of excitation are only weakly coupled. The spatial motion around the ideal lattice point would not influence too much the up/down position of the magnetism of the nuclear spin and vice versa. The spatial motion has a squared average of velocity <v2> = 3MT1, and the spins will be populated as N+/N- = exp{-2Hμ/T2}. All experiments show that after some time T1=T2; but it is very easy to disturb the equipartition. The simplest way is to reverse the external magnetic field H. Then the spin distribution becomes of inversely populated, or, by other words,

              T1 = -T2 = Tlab = 293 K                                                                                                          (4.2)

And indeed the negative spin temperature, followed by a gradual equilibrium, first with T2 going to -∞ then from +∞ towards +293 K, can be clearly observed. The process takes minutes [25].

            So the two reservoirs may have two different temperatures. However, this is a consequence of the weak coupling between nuclear magnetic momenta and the spatial motion of the ions, and not of a declaration of two independent reservoirs, or saying "Abrakadabra". If you push down the piston, the gas in the cylinder will become denser. A gas is a bunch of molecules, with or without forces between. If we knew the interactions, we could calculate the reaction of the gas to compression. If we do not yet know them, at least some characteristic data of the extra reservoir can be determined.

            Perform a slow compression. We are told that the temperature is higher than before Change, even if not much higher. So it is possible we see Equipartition in Action. The energy of the compression work goes first into the "weird reservoir" (E2) and then seeps into E1 as well. I would be very, very surprised if the evolution equation of the process were not approximately

              dE1/dt = (other trivial thermo terms)  -(E1-E1,eq)/τ                                                                    (4.3)

where E1,eq is the value belonging to

              T1(E1,E2,V,N) = T2(E1,E2,V,N)                                                                                              (4.4)

In simple cases the equilibrium state is somewhere at E1 ~ E2. Here τ is the relaxation time, and that can be observed even with unaided eyes. For a similar problem but in cosmology see [27], for a better elaborated analogy see [28].

            If the Alien Space Bats established (or much enhanced) an intermolecular interaction damping the thermal motion of gas molecules or sticking them transiently together and releasing them with the relaxation time τ, that τ must be at least in the seconds range, otherwise internal combustion engines would work. If it is really in the seconds range then wind guns still work. If it is in minutes range then even they do not work. However, it is rather a very serious assumption that mere intermolecular forces could keep lots of energies for minutes. In our OTL physics these forces are most often van der Waals forces from the tails of the electromagnetism in molecules. One way to feel them is the polarisation behind solvation processes (which could not seriously change otherwise pre-Change Biology would have stopped at change). Another example is the H-bridges, e.g. in peptide chains establishing the tertiary structures of enzymes, or between the two chains of a DNA "ladder". In these cases the OTL intermoleculary forces are not of very long range and the characteristic energy of the interaction is a mere ~0.05 eV, which is ~500 K in temperature.

            Such forces are behind the familiar vapour-liquid phase transition as well. And we can produce non-equilibrium phase transitions without any high-tech, simply by heating, cooling, compressing or decompressing the matter really fast.

            So maybe the Alien Space Bats can be circumvented by means of tricky heat engines. Or, maybe they have not created a "second reservoir" at all. There is an even more traditional way; of course I, here in OTL, cannot perform the decisive experiments instead of Ken Larsson or the Physics Department of OSU at Corvallis.



            Assume now that some interactions have indeed changed (otherwise the Fire would not have died on 17th March, 1998 in ETL) but in the simplest way (according to Occam's Razor, so the Simplest Way is the simplest one which is enough to describe the event). So let us try still with the minimal extensive set {V,E,N}. Then the independent extensive densities are e and n, and the density of the thermodynamic potential is

              s = s(e,n)                                                                                                                                (5.1)

            Thermodynamics does have a canonic structure, so we can substitute one or more intensive variable instead of the canonical conjugate extensive, if we introduce an appropriate new potential as well. Also, if there is a single energy variable, we can switch from entropy as potential and energy as variable to energy as potential and entropy as variable. So, let us make this, second, transformation first, and then let us substitute entropy with the conjugate temperature; and finally let us go to densities [19]. Then the potential density is the density of the free energy f:

              f = f(T,n)                                                                                                                                (5.2)

              s = -f,T                                                                                                                                   (5.3)

              p = nf,n - f                                                                                                                              (5.4)

              e = f - Tf,T                                                                                                                             (5.5)

Obviously f(T,n) carries all the quasistatic information about the thermodynamic behaviour of the system.

            Before the Change at 1 atm pressure and 293 K temperature all simple real gases (as air, water vapour, carbon dioxide and such were quite near to the ideal gas limit, i.e.

              fnTln(n) - (3/2)nTln(T) + CnT                                                                                             (5.6)

where C is some combination of molecular weights, statistical factors & such and is not important for mechanical behaviour. From (5.6) you get two equations of state:

              p = nT                                                                                                                                    (5.7)

              e = (3/2)nT                                                                                                                             (5.8)

(5.7) would not be true if the molecules occupied a substantial part of the whole volume (which is definitely not true: at usual circumstances air is almost 3 orders of magnitude less dense than water), or if the intermolecular interactions were quite strong (which they were not). I do not believe that the Aliens changed the volumes of the molecules (then, e.g., the lungs would operate strangely); but they might change the intermolecular interactions (I do not yet know, how; but that knowledge is not needed for discussing the thermodynamic behaviour).

            Now, Ken Larsson's observations resulted in:

              lim n→0 p(n,T) ~ n

              lim n→no p(n,T) = ∞

              lim T→0 p(n,T) ~ T

              lim T→∞_ = nTo                                                                                                                        (5.9)

where no is sime characteristic density well above normal air density but well below the characteristic densities of liquids; and To is a temperature probably below the pre-Change critical temperature of water (640 K).

            One could try with Ansätze for approximate free energy functions without any guess for the intermoleculary forces behind, even with only paper and pen. To demonstrate this, here I start with the simplest form

              p(n,T) = a(n)b(T)                                                                                                                    (5.10)

Maybe it will not be enough (alas, the information is on an other TimeLine) but then it is rather straightforward for everybody to generalise the Ansatz.

            With (5.10) eq. (5.4) can be integrated. Let us call A(n) as follows:

              dA/dn ≡ a(n)/n2                                                                                                                      (5.11)


              f(n,T) = n[A(n)b(T) + c(T)]                                                                                                     (5.12)

Now, for the internal energy density eq. (5.5) yields

              e(n,T) = nA(n)(b(T)-Tdb/dT) + n(c(T)-Tdc/dT)                                                                      (5.13)

where the constraints (5.9) give similar ones for a(n) and b(T).

            Obviously A(n) diverges approaching n=no, but this is not a surprise at all, and simple van der Waals systems do it (although they do it after phase transition). It is also obvious that the system must have a divergent thermal capacity at high temperatures otherwise the compression would increase the temperature; however now eq. (5.13) shows that the single energy reservoir may take extra energies if c(T) is tricky enough.

            Maybe the simple Ansatz (5.10) will be enough, maybe not. Even, you may choose different f(n,T)'s leading to different fates of the Emberverse TL after CY 23, which may be fun.

            Thermodynamics is almost solely phenomenologic, but in its own territory it is very strong.



            Earlier illuminating discussions with K. Martinás are acknowledged.



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