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Areas of science are defined by what they study. Electromagnetism studies electric / magnetic forces, astronomy studies stars etc.

The thing studied by thermodynamics is entropy. What is interesting is that this concept in non-empirical. Clausius (one of the giants in the field of thermodynamics) said that entropy cannot be measured.

Science deals with things that can be measured in physical experiments.

Does that mean that thermodynamics is not science? How can one reconcile the fact that thermodynamics is well-established as a branch of physics if it deals with a number of topics like Gibbs free energy, entropy, and enthalpy which are not physical in the same way that matter is?

J D
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Dennis Kozevnikoff
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  • See e.g Alessandro Bettini, A Course in Classical Physics 2 Fluids and Thermodynamics (Springer, 2016), page 49: "Thermodynamics developed historically after mechanics, mainly in the XIX century. Development was motivated by two main needs, both outside of pure physics. The first motivation was the search to understand how the leaving creature “produces” energy; the second was the desire to develop engines capable of transforming heat, generated, for example, by the burning of coal, to produce mechanical work which otherwise had to be done by humans or animals. 1/2 – Mauro ALLEGRANZA May 03 '23 at 15:13
  • However, thermodynamics is not important for engineering and biology alone, but represents one of the fundamental chapters in physics." 2/2 – Mauro ALLEGRANZA May 03 '23 at 15:13
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    Is entropy really "not measurable"? Even Wikipedia contends it is measurable. – Frank May 03 '23 at 15:20
  • @Frank It can be descriptively compared between systems but hardly measured in terms of an objective, ordinal scale. – Philip Klöcking May 03 '23 at 15:35
  • @PhilipKlöcking Surprising. There seems to be a formula for Gibbs entropy in statistical thermodynamics. Maybe in classical thermodynamics we have access only to change in entropy? But if we can measure those, that should be enough to qualify entropy as "measurable", shouldn't it? – Frank May 03 '23 at 15:43
  • Thermodynamics studies averaged effects of collective behavior of multiple identical physical elements (typically, particles). They are perfectly measurable in experiments (temperature, pressure, etc.). Entropy is a function of measurable quantities, just like energy is. "Science deals with things that can be measured in physical experiments" is false even if we narrow it down to empirical sciences. There are also [formal sciences](https://en.wikipedia.org/wiki/Formal_science). – Conifold May 03 '23 at 17:36
  • Thermodynamics is not the study of entropy; it's the study of of the relationship between heat and work, and entropy is just one way of formulating part of that relationship. And I assume what Clausius meant is that absolute entropy cannot be measured. Changes in entropy certainly can be measured. – David Gudeman May 03 '23 at 18:00
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    Einstein on Thermodynamics: “It is the only physical theory of universal content, which I am convinced, that within the framework of applicability of its basic concepts will never be overthrown.” – CriglCragl May 03 '23 at 21:08
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    Please give the Clausius quote. Entropy is an emergent property, perhaps that is your issue. We can regard it in information transfer terms, as Shannon showed. We find information flow & limits are crucial to quantum mechanics (wf collapse) & relativity (lightspeed), & it's likely information is more fundamental, not less. – CriglCragl May 03 '23 at 21:10
  • @Frank: Entropy is always measured in terms of change, because 'hidden' structure & complexity can mean entropy is present which has not been influencing the system. If you consider Shannon's picture, we treat the initial system as 'signal', & rise in entropy as signal loss. We can't get more signal than we started with, but there might have been hidden encoded extra signal that we didn't recognise at first. – CriglCragl May 03 '23 at 21:20
  • In any case, it seems farfetched to say that "because entropy is not measurable, thermodynamics is not science". – Frank May 03 '23 at 22:29
  • @Frank Indeed. There's more to science than just mindless measurement. ; ) Rational appraisal of scientific theory using confirmation, verification, and falsification absolutely play a role, as speculative as such enterprises are (presuming you don't legislate speculation out of scientific argument). – J D May 04 '23 at 14:42
  • Added a clarificatory question to try to stave off closure of an obviously philosophical question with relevance to both the philosophy of science and physics. – J D May 04 '23 at 14:45

3 Answers3

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Thermodynamics is not just the study of entropy. It is what you get when you apply the laws of motion to statistically large ensembles of particles undergoing random collisions.

There is no "entropy gauge" that you can stick into a tank of hot gas to measure its entropy content in the same sense that there is no "net present value gauge" that you can thrust into a ensemble of assets or a pile of money. If you attempt to derive a thermodynamic description of some process involving the extraction or addition of energy or work to or from a system, you'll get the wrong answer if you do not take entropy changes into account.

The concept of entropy emerges from the fundamental mathematical derivation of the statistical behavior of the ensembles I mentioned above, which derivations are based on first principles and backed by experiment.

Rest assured that thermodynamics is an extremely well-developed branch of physics and is indeed fundamentally scientific. As one of my engineering professors liked to say, this is true even though you cannot see the pipe that carries the entropy into or out of an automobile engine, nor measure its flow rate with a gauge bearing numbers on a dial.

niels nielsen
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  • You can see the pipe that carries fuel in to the engine, and the pipe that carries disordered fuel out again. Fossil fuels are stored sunlight, and the energy is put in to the star by gravity, the ultimate cause of everything that happens in the universe. – Scott Rowe May 03 '23 at 22:41
  • The concept of entropy existed before statistical mechanics. It was originally used in the analysis of steam engines. The statistical explanation came somewhat later. https://www.scholarpedia.org/article/Entropy – Boba Fit May 03 '23 at 23:40
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Entropy is not directly measurable. That is, we don't have a device that lets us stick a probe in a bucket of water and read off "12.7 Joule-Kelvin." (The physical quantity of entropy is energy x temperature, Joule-Kelvin.)

Entropy is a thermodynamic state variable. That means it is a characteristic of a particular arrangement and type of stuff. We calculate the amount of entropy based on the type and amount of stuff and the arrangement. The arrangement includes such things as the temperature and the pressure of the stuff. In some interesting situations there are other parameters that have an impact on entropy, such as magnetic orientation of the nucleus of atoms involved in an MRI machine.

There are other quantities that have this sort of context. The energy in a gas, for example, is not directly measurable. We do not have a probe that we can stick in a gas and get "12.7 Joules." We measure other parameters and calculate the energy. Some of those other parameters are temperature and pressure. In many situations there are other factors such as molecular structure.

And, indeed, the kinetic energy of an object in motion is such a quantity. We don't have a measurement that will read off "4.8 Joules" for a thing like a baseball. We measure the speed of the ball and the mass of the ball. Then we calculate the kinetic energy.

In fact, there are many important physical quantities that have this sort of context. And there are many more that are macroscopic indicators of microscopic conditions that are not simple to observe. Temperature, for example, is a macroscopic indicator of microscopic motion of molecules. For ordinary situations it is a challenge to observe directly the motion of molecules. However, we have thermometers to measure temperature.

Some parts of science have some extreme cases of this.

For example, in electrical circuits, there is a thing called the electric potential. You observe only the difference in potential from one point to another. You do not observe the absolute potential. You observe the difference between one side of an electrical plug and the other, you cannot observe the absolute value of either side.

For example, in quantum mechanics (QM), the phase of a particle is deemed to be entirely impossible to observe directly. Only differences in phase can be measured. As for example, between one location and another. The absolute value of the phase cannot be observed.

It is even more extreme in QM when the wave function is considered. The wave function gives the probability of a particle being observed at a location. The wave function itself cannot be observed directly . And only statistical inferences can be made on the basis of a finite number of observations.

So it is by no means unusual in science to have physical quantities that are not directly measurable. It should not cause us to be perplexed.

Boba Fit
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    Entropy has the dimensions of energy divided by temperature and units of Joule per Kelvin. – Bumble May 03 '23 at 23:55
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Science deals with things that can be measured in physical experiments.

Very true, but I think most philosophers would contend that given the robust literature on demarcation, various sciences as sociological extensions of personal empirical knowledge is a little broader than "measuring physical things". For instance, to what extent are measurements of physical experiments dependent upon our perceptions? To some extent, surely, and according to a critical realist, there are elements of measurement that are a function of theory-laden, rational thought such that it might be useful to think of some of science as being epistemologically derived from a certain well-regarded physicalist ontology. That is, science has a rational component that extends physical measurements. Mathematical physics as an enterprise accepts that not everything that can be declared real can be touched with fingers or held alongside a ruler.

Is thermodynamics science?

Absolutely. Science is more than mere measurement. It involves a certain deal of philosophical grounding related to building and establishing a web of belief regarding that which can be measured, not all of which is physically tangible or admissible by a correspondent theory of truth. There are many scientific concepts that involve something more than mere measurement. Take for instance the notions of wave packets and wave-particle duality in quantum mechanics. Unlike a banana, the ontological existence of electrons is a tad more complicated than holding up a ruler to an electron. It requires a series of experiments which establish and corroborate various mathematical theories all of which when taken together make a good argument for the existence of an electron, despite the fact that we can directly see an electron in the same way directly see a banana.

The lesson to be learned here is that the philosophy of science is much more sophisticated than simple empiricism or the more sophisticated British empiricism both of which are philosophically historical. Modern philosophy of science underwent a vast transformation with logical positivism and empiricism and into a brave new world of post-positivist scientific thinking by late Wittgenstein, Sellars, and Quine according to Richard Rorty.

From Sellars "Empiricism and the Philosophy of Mind":

empirical knowledge, like its sophisticated extension, science, is rational, not because it has a foundation but because it is a self-correcting enterprise which can put any claim in jeopardy, though not all at once.

Thus, science is more than just physical measurement, it is the joint venture by scientists to argue and discuss and theorize; thermodynamics, then is a very well established physical theory according to physicists.

J D
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    Oh, well. I do think that you assertion that electrons aren't real, which I asked you for a justification, isn't inherently bad intuition. In fact, it's good philosophical intuition because it anticipates more sophisticated philosophical appraisal of scientific methodology, particularly from an instrumentalist perspective. Of course, most "philosophers" suffer from knee-jerk physicalism. ; ) – J D May 04 '23 at 17:02