19 Aug 2015

Somers-Hall, (5.2), Deleuze’s Difference and Repetition, ‘5.2 Thermodynamics and Transcendental Illusion (222–9/280–8)’, summary

by Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH and Difference and Repetition as DR.]

Summary of

Henry Somers-Hall

Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide

Part 1
A Guide to the Text

Chapter 5. The Asymmetrical Synthesis of the Sensiblence


5.2 Thermodynamics and Transcendental Illusion (222–9/280–8)



Brief summary: 

For Deleuze, difference is difference in intensity. We see in Carnot’s thermodynamic ideas, particularly the second law of thermodynamics, the energetic power of intensive differentials. A thermodynamic system has more power to perform its work when there is a greater difference of temperature between its input heat and its output or environmental cold. However, in other ways, thermodynamics is fundamentally incompatible with Deleuze’s metaphysics. Thermodynamics thinks there is entropy in thermodynamic systems whereby heat differentials tend to equalize over time as systems tend toward a state of homogenized disorder. But Deleuze notes that there is another factor that thermodynamics is missing, which is the generation of the intensive differentials. Thermodynamics cannot for example explain the generation of life, in which there is movement toward more and greater differentials as the organism diversifies and becomes increasingly heterogeneous and organized rather than homogeneously disordered.


Deleuze opens chapter 5 of DR with a discussion of thermodynamics, which “deals fundamentally with the properties of heat” (SH 167). Carnot is the founder of this field. “His main discovery was that the efficiency of even an ideal frictionless engine was dependent on the difference between its hottest and coldest parts: the greater the difference, the greater the efficiency” (167). SH will “explore Deleuze’s engagement with thermodynamics by looking at three questions. First, what is the transcendental principle that thermodynamics embodies? Second, why does this transcendental principle reinforce rather than overturn good sense? And third, why does Deleuze consider this transcendental principle to be a transcendental illusion?” (167).

So we begin with the “transcendental principle of thermodynamics” which is the second law of thermodynamics. [It seems to be saying that heat always moves from warm to cold places, unless another factor intervenes:]  “The transcendental principle of thermodynamics rests on the second law of thermodynamics. This is, in Clausius’ formulation, the claim that ‘heat does not pass from a body at low temperature to one at high temperature without an accompanying change elsewhere’ (Atkins 2010: 42)” (SH 167). What interests us is the insight of Carnot’s underlying this law.  In order to increase a thermodynamic system’s ability or power to conduct its work, we can either increase the temperature of for example the steam going into the system or else we may decrease the temperature outside it. [I am not sure I understand how this works. Let us just quickly look at some diagrams of a Serling Engine that I have found online. The first one is from Chris Woodford at ExplainThatStuff!:


Here is quotation of Woodford’s explanation:

1) Heating and expansion: The gas starts off on the left in the hot end of the cylinder. It's heated by the fire (or other heat source) so its pressure rises and it expands, absorbing energy. As the gas expands, it pushes the work piston to the right, which drives the flywheel and whatever the engine is powering. In this part of the cycle, the engine converts heat energy into mechanical energy (and does work).

2) Transfer and cooling: The displacer piston moves to the left and the hot gas moves around it to the cooler part of the cylinder on the right. Both pistons now move to the right together, so the volume of the gas remains constant as it passes through the regenerator (heat exchanger), giving up some of its energy on the way.

3) Cooling and compression: Now the gas arrives in the coldest part of the cylinder, by the heat sink. Here it cools and contracts, giving up some of its heat, which is removed by the heat sink, and both pistons move inward.

4) Transfer and regeneration: The displacer piston moves to the right and the cooled gas moves around it to the hotter part of the cylinder on the left. The volume of the gas remains constant as it passes back through the regenerator (heat exchanger) to pick up some of the heat it previously deposited. The gas is now back where it started and the process can repeat.
(diagram and text taken gratefully from: Chris Woodford at ExplainThatStuff!)

Here is another animated diagram of a Stirling Engine from the course webpage of David Wallace’s and Douglas Hart’s MIT course, Mechanical Engineering Tools.


Here is quotation from their webpage:

Stirling engines are unique heat engines because their theoretical efficiency is nearly equal to their theoretical maximum efficiency, known as the Carnot Cycle efficiency. Stirling engines are powered by the expansion of a gas when heated, followed by the compression of the gas when cooled. The Stirling engine contains a fixed amount of gas that is transferred back and forth between a “cold” end (often room temperature) and a “hot” end (often heated by a kerosene or alcohol burner). The “displacer piston” moves the gas between the two ends and the “power piston” changes the internal volume as the gas expands and contracts.

Air in the engine is cyclically heated (by an alcohol burner) and expands to push the power piston (shown in blue) to the right. As the power piston moves to the right, the yellow linkage forces the loose-fitting, red "piston" (on the left half of the machine) to displace air to the cooler side of the engine. The air on the cool side loses heat to the outside world and contracts, pulling the blue piston to the left. The air is again displaced, sending it back to the hotter region of the engine, and the cycle repeats.

The Stirling engine cycle can also be used “in reverse”, to convert rotating motion into a temperature differential (and thus provide refrigeration).

(Image and text taken gratefully from David Wallace’s and Douglas Hart’s MIT course, Mechanical Engineering Tools, webpage)

Perhaps the idea here is that we can make the engine work harder by increasing the heat that pushes the piston. Or, consider also if on the other side the gas in the chamber were cooler. Perhaps that would mean that the tendency for the heated air to expand and push the piston to the colder side would be greater, and thus with the same amount of heat input there would be more force to the expansion. Or, perhaps what we should be interested in is the third step of cooling and compression, when “The air on the cool side loses heat to the outside world and contracts,” and so were the outside world colder, perhaps this contraction would be more forceful. Probably I have this wrong, but what we are looking for is the work being greater were the difference between hot and cold to be greater. What is important here philosophically is that difference in intensity, that is in this case, the difference between two temperatures, is what is responsible for the work. Deleuze also claims that intensity is difference, perhaps because for example temperature is already a matter of difference or variation, but I am not sure.]

Now, this statement rests on a central insight by Carnot that, when we look at a system, the work that the system is able to do is not dependent on the heat entering the system, but rather on the difference between the temperature entering the system and the temperature leaving the system. Thus, if we wished to improve the efficiency of, say, a steam engine, we could do this either by increasing the temperature of the steam that powers it, or alternatively we could reduce the temperature of the environment surrounding the generator (although only the first of these alternatives is in general really practical). The important implication of this is that what allows work to be done by a system is not intensity (temperature in this case), but rather difference in intensity (and in fact Deleuze makes the stronger claim that ‘intensity is difference’ [DR | 223/281])
(SH 167-168)

[I do not follow the next points so well. The next one seems to be that because difference in temperature is needed for the engine to work, difference is needed for anything whatsoever to happen or to appear. “Carnot’s work shows that if the input and output energies of an engine were equal, the efficiency of the engine would drop to zero. Thus, difference is fundamentally implicated in ‘everything which happens and everything which appears’ (DR 222/280)”. But I do not know how to draw that inference yet. Perhaps the idea is that for something to appear or to happen, there needs to be a change, and for there to be a change, there needs to be imbalance and thus difference in intensity like between hot and cold. This also holds for phenomenal appearing. The next idea seems to be that were thermodynamics to stop here at the second law, then it would be compatible with Deleuze’s metaphysics of difference. But thermodynamics has other notions which are not compatible with Deleuze’s philosophy, namely, entropy and the equalization of differences.]

Carnot’s work shows that if the input and output energies of an engine were equal, the efficiency of the engine would drop to zero. Thus, difference is fundamentally implicated in ‘everything which happens and everything which appears’ (DR 222/280). In line with Deleuze’s distinction between the transcendental and the empirical, Deleuze draws from this the principle that ‘every phenomenon flashes in a signal-sign system’ (DR 222/280). Just as the difference in the intensity of temperature gives rise to work, Deleuze’s claim is that more generally, differences in intensity manifest themselves as qualities in the phenomenal world. If this were the final result of thermodynamics, then clearly it would provide a model of physics commensurate with Deleuze’s metaphysics. Deleuze claims, however, that thermodynamics betrays its own principle of difference through the introduction of entropy, and the concomitant equalisation of differences.

But such thermodynamic systems are never perfectly efficient, since some energy will always be lost rather than put to work. For example, a steam engine heats its surrounding air, which is heat lost outside the system. [I am not sure I completely follow the next point about refrigeration. The important idea seems to be that refrigerators are open systems, since they exchange heat with the environment (I am not sure how they work, but perhaps what they are doing is keeping the inside cold by pushing the heat out of the system). The other important idea here seems to be that it maintains a temperature differential, I suppose between the inside of the system and the outside, where instead of heat going to the cold, that is, moving from outside to inside, it instead moves from cold to hot, that is inside to outside. I am not sure why that is important, but maybe the idea is that the refrigerator seems to act against forces of entropy. However, the whole universe, which is a closed system since it has no outside to it, will not be able to maintain temperature differentials, since they will all tend to equalize. This means eventually all temperatures will homogenize. It also means that time is moving in the direction toward this ‘heat death’.]

If we return to Carnot’s engine, we can see that useful work cannot be done with total efficiency by the engine (except in the impossible situation of a difference between absolute zero and an infinite temperature). What happens to the heat that isn’t converted into work by the engine? Well, this energy is introduced into the output reservoir as heat (just as a steam engine heats the environment as well as moving the train). Thus, in the process of doing work, the system reduces the difference between the two temperatures. It is possible to reverse this process within the system itself by doing work (a refrigerator, for instance, is able to reduce the temperature of objects placed within it), but this work itself will not be totally efficient. We can see this in the case of the refrigerator if we take into account its environment. In order to create a temperature differential, it requires a flow of energy from outside of it. So while the refrigerator allows heat to flow from bodies at low temperature to bodies at higher temperatures, this is only as a result of an interaction with its environment whereby energy is supplied to it by equalising a temperature differential elsewhere (the power station, for instance). In this case, a temperature differential is maintained in the system because the system exchanges heat with its environment (it is what is known as an open system); but if we look at the universe as a whole as a system, we can see that in this case, there is no further environment with which it can exchange energy (it is a closed system). Now, given the first law of thermodynamics, which states that there is a fixed quantity of energy in the world, then, over time, as various processes in the universe do work, more energy will be lost as heat as a result of inefficiency. Eventually, | the differences in intensity that make work possible will themselves be equalised by this loss of heat, leading to what Boltzmann called the ‘heat death’ of the universe, as it becomes a homogeneous field of constant temperature. This, according to thermodynamics, is what gives the ‘arrow of time’ a direction: time only moves in one direction because certain processes are irreversible.

Deleuze will now relate these notions to the good sense and common sense. [I do not follow this part very well. For this we need to recall that “common sense refers to the indeterminate structures of the subject and the object.” But I do not remember what this indeterminacy is, so I am missing most of the reasoning here. Maybe the idea is that the world we encounter, and we ourselves, are not determinate but secondarily obtain determinations through our faculties’ cooperating to recognize objects and ourselves. The basic idea (the reasoning behind which I do not grasp at all) seems to be that if we regard the world as being made of indeterminate objects and subjects, then we will also think that the world is made of properties which are differential relations that dissipate, equalize, and homogenize like heat is thought to do in thermodynamics. Let me quote it so we have it right:]

Deleuze relates this result to the structures of good sense and common sense. As we saw, common sense refers to the indeterminate structures of the subject and the object. Now, we never actually encounter indeterminate objects, but rather a field of objects, each with diverse properties. It was good sense that related these various properties together into a hierarchy, such as the tree of Porphyry, affirming their ordered relation to the object as an instance of an object in general. Here, thermodynamics provides a physical instance of this process. If the properties of objects are defined by differences in intensity, then thermodynamics shows that over time, these differences, and hence the properties they sustain, will be cancelled out. The heat death of the universe, with its model of total homogeneity, is the final affirmation of the true nature of the world as grounded in indeterminate subjects and objects, despite the transient appearance of diversity that appears to signal otherwise [the following up to citation is Deleuze quotation, and the bracketed text to follow is SH’s].

[Good sense] ensures the distribution of that difference in such a manner that it tends to be cancelled in the object, and because it provides a rule according to which the different objects tend to equalise themselves and the different Selves tend to become uniform, good sense in turn points towards the instance of a common sense which provides it with both the form of a universal Self and that of an indeterminate object. (DR 226/285)

Thus, organised systems tend to fall into disorder over time as the intensive differences that allow structure and useful work to take place give way to a disordered field lacking in any organising differences in intensity.
(SH 169)

Deleuze thinks this thermodynamic model is a transcendental illusion. This is because it assumes that the differences in intensity are pregivens rather than needing to be generated and distributed in the first place. These theories were invented by people whose interest was in isolated systems that are brought into interaction with other systems, like engines brought into relation with their environment as they are put to work. [The next idea seems to be that when you link up two systems, disorder increases because you have more variables and factors interacting.] But we also find that systems tend to isolate themselves from their environments and instead of increasing entropy, decrease it, as in the case of living beings and their evolution. Thermodynamics cannot account for the emergence of life, which acts contrary to entropy, [since it generates more differentials, heterogeneities, and variations rather than decrease them into a state of disordered homogeneity.]

Finally, why is this model considered by Deleuze to be a transcendental illusion? As Deleuze notes, the theory of thermodynamics is a partial truth, but it becomes a transcendental illusion when we attach ‘the feeling of the absolute to [this] partial [truth]’ (DR 226/284). This partial truth operates within the framework of ‘forms of energy which are already localised and distributed in extensity, or extensities already qualified by forms of energy’ (DR 223/281). As such, it assumes the differences in intensity as already given as preformed. What is missing | from the thermodynamic model is an account of the genesis of these intensive differences in the first place, and their localisation in particular regions of extensity (space). As Deleuze puts it, ‘perhaps good sense even presupposes madness in order to come after and correct what madness there is in any prior distribution’ (DR 224/283). Stewart and Cohen argue similarly in their study of complexity theory that the classical model of thermodynamics works well for the kinds of systems its inventors were interested in (Stewart and Cohen 2000: 258). These situations were where we have an individuated, isolated system that is brought into interaction with another system (the engine being brought into relation with its environment, or in Boltzmann’s classic example, the mixing of two gasses). In these cases, the amount of disorder increases because the number of systems has reduced, just as ‘a children’s party with ten children is far more chaotic than two parties with five each’ (Stewart and Cohen 2000: 258). If we move away from the mechanical models of the nineteenth century, we find that frequently systems are not just put into relation to their environment, but are also capable of isolating themselves from this environment. Life, for instance, is a process of individuation whereby new systems emerge, and with this emergence, decrease the amount of entropy present in the world: The features that are of interest when studying steam engines, however, are not particularly appropriate to the study of life . . . For systems such as these, the thermodynamic model of independent subsystems whose interactions switch on and off is simply not relevant. The features of thermodynamics either don’t apply, or are so long-term that they don’t model anything interesting. (Stewart and Cohen 2000: 259) While thermodynamics provides an account of processes affecting preconstituted systems, qualities and extensities, it does not account for the emergence of these systems, qualities and extensities in the first place. Much of the remainder of the chapter will attempt to show how intensity is central to this process of constitution.
(SH 169-170)

Citations from:

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.

Or if otherwise noted:

Deleuze, Gilles. Difference and Repetition, trans. Paul Patton, New York: Columbia University Press, 1994/London: Continuum, 2004.

Atkins, Peter (2010), The Laws of Thermodynamics: A Very Short Introduction, Oxford: Oxford University Press.

Stewart, Ian, and Jack Cohen (2000), The Collapse of Chaos: Discovering Simplicity in a Complex World, London: Penguin Books. Tomarchio, John (2002), ‘Aquinas’s Concept

Engine text and diagrams taken gratefully from:

Chris Woodford at ExplainThatStuff! “Stirling enginges.”

David Wallace’s and Douglas Hart’s MIT course, Mechanical Engineering Tools. http://ocw.mit.edu/courses/mechanical-engineering/2-670-mechanical-engineering-tools-january-iap-2004/study-materials/






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