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So I was going through callen's thermodynamics book and their he says that thermodynamics is only applicable to systems which are in equilibrium and that naturally raised a few questions in my mind

Is thermodynamics really never applicable to systems which are not in equilibrium, if so why should such a restriction exist?

And also it might sound silly but why is the theory called "thermodynamics"- specifically the "dynamics" part?

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    $\begingroup$ Could you give the reference for the quote? $\endgroup$ Apr 28, 2019 at 12:28
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    $\begingroup$ Wouldn't that be "thermostatics"?? ;-) $\endgroup$ Apr 28, 2019 at 13:16
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    $\begingroup$ @PeterA.Schneider No not necessarily, since equilibrium can be dynamical. For instance, the quasi-static model of a star is in dynamical equilbrium. $\endgroup$ Apr 28, 2019 at 15:11
  • $\begingroup$ A typical dynamic example system used in thermodynamics is an internal combustion engine using the otto cycle. See en.wikipedia.org/wiki/Otto_cycle $\endgroup$ Apr 29, 2019 at 8:35

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It entirely depends on what you think "thermodynamics" is.

The traditional idea of thermodynamics dealing with systems whose macrostate can be fully described by e.g. temperature, pressure and volume indeed only applies to systems in equilibrium. Of course, as an approximation it also applies to systems "not far" from equilibrium, for some suitable notion of "not far", explaining its success in describing nevertheless a plethora of phenomena that occur in the real world.

However, non-equilibrium thermodynamics also exists, and is well and alive as a subfield of both classical and quantum physics. Its methods, however, differ strongly from what is commonly referred to as "thermodynamics" in introductory textbooks.

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    $\begingroup$ Am I wrong in believing that the heat flow equation is then not a part of thermodynamics cause it describes situation when temperature of a system has not yet reached equilibrium? $\endgroup$
    – Metric
    Apr 28, 2019 at 10:37
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    $\begingroup$ @Lucifer I don't think it is useful to say that equation is or is not "part of thermodynamics". Why does it matter what "part" of physics an equation "belongs to"? The heat flow equation is a rather fundamental differential equation whose functional form appears in a lot of different contexts. However, I would argue that the heat flow equation is "classical equilibrium thermodynamics" in the sense that it deals with temperature, and so must assume local equilibrium along the flow in order for temperature to be well-defined. $\endgroup$
    – ACuriousMind
    Apr 28, 2019 at 10:41
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    $\begingroup$ The other problem is I'm entirely new to thermodynamics so I don't really know what "i think thermodynamics is" but rely on books and peoples to let me know what thermodynamics is and different author and different people seem to have different notions about so it's getting a bit confusing. Can you tell me a little about the absolute fundamentals? I believe I can understand the rest of it once someone clearly lays down the fundamentals. $\endgroup$
    – Metric
    Apr 28, 2019 at 10:42
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    $\begingroup$ @Lucifer I'm afraid free-form introductions to a topic are not what this site is for, especially not its comments. However, people having slightly different notions of what exactly a sub-field entails is something you'll encounter all over physics and something you'll have to get used to. In the end, the laws of nature that you learn do not care for the categories we humans put them in. If you learn how heat flow works, then you know how heat flow works! It doesn't suddenly become wrong if a few years from now you decide that it isn't "real thermodynamics". $\endgroup$
    – ACuriousMind
    Apr 28, 2019 at 10:50
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    $\begingroup$ @Lucifer Perhaps it is easy enough to think about "equilibrium thermodynamics" as the times when, at a given location in space, there is only one temperature value. Non-equilibrium is when a given location in space has multiple temperatures, for example, a translational and vibrational temperature, that are different. The heat conduction equation only has one $T$ and so it is equilibrium thermodynamics, even though the system is not in equilibrium. In other words -- "equilibrium thermodynamics" is talking about molecular-scale equilibrium, not macro-scale equilibrium. $\endgroup$
    – tpg2114
    Apr 28, 2019 at 13:29
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Strictly speaking, thermodynamics only describes systems at equilibrium or systems that undergo some change; in the end, they have time to relax back to an equilibrium state. The signature of a thermodynamic system is the massive reduction of the number of degrees of freedom required to describe the state of the system.

Nonequilibrium is a weak characterization, and one can distinguish different departure levels from thermodynamic equilibrium.

For example, hydrodynamics corresponds to a case where, due to a macroscopic movement of the fluid, if the flow is not too complex, a three-dimensional velocity vector field is required, in addition to a couple of thermodynamic scalar fields which describe the local thermodynamic equilibrium.

The case of thermodynamic systems brought slightly out of equilibrium is also interesting. In that case, studying the fluxes that try to restore equilibrium and get information about transport coefficients is possible.

However, one has to take into account that significant departures from equilibrium are possible, basically requiring to go to detailed descriptions using a huge number of degrees of freedom.

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Good question. The study of thermodynamics is usually between eqilibria. But these take many shapes. And they are yours to define - a state of chemical equilibrium is for instance a state where we define that a forward reaction is equal to its reverse reaction. But we can define only forward flux as a state - an adiabatic state is where a chemical reaction is isolated from heat and work from the outside - so that the only place for heat generated by the reaction is the heatflux of it's reactants. This is certainly not a chemical equilibrium per se but it is a defined state. What is very useful for aspiring thermodynamicists is that we can daisy-chain states together even if we do not know the relationship between state A and state C, as long as we know something about the relationships A and B in addition to B and C, we can go that way.

So, most of thermodynamics are basically defining different states of matter and energy and using known relations between them - figuring out what happens next. There is of course also an entire field studying what happens when we are not able to define the states well - non-equilibrium thermodynamics, but that is not for the faint of heart.

The name thermodynamics is old - from the time of Lord Kelvin, Lavosier and Lagrange and that bunch. Back then, you studied heat - where does heat go? If you burn something, what is the heat generated? How much capacity for heat does a substance have? How much hotter does it get with a fixed amount of heat? We inherit a lot from these old geezers, they were quite bright. We still call energies related to chemical reactions "Heat of Formation" - although most people use the word "Enthalpy". There are many of these "Heats" - sublimation, solidification, mixing... The study was thus called Thermo-dynamics - the movement of heat!

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When dealing with thermodynamics, you are interested in knowing the values of thermodynamic variables such as temperature, pressure, volume, entropy, etc of the system, and we assume that these quantities have uniform values throughout the system. For non-equilibrium systems, this assumption may not hold. For example, if you heat a liquid in a container, different fluid parcels may have different temperatures.

To answer your question about the nomenclature, thermodynamics evolved when people started studying heat engines and how "heat moved" from one body to another. So heat(thermo) and movement(dynamics).

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The "thermodynamics" of the 19th century was mostly about static systems in thermodynamic equilibrium. It was formulated to calculate the initial and final entropies when a system evolved from one equilibrium state to another. In this older view of thermodynamics (that would be better referred to as thermostatics) there is no direct relationship between a natural process (e.g. chemical reactions, conduction of heat) and the rate at which entropy changes.

During the 20th century, physicists like Onsager, Eckart (see The Thermodynamics of Irreversible Processes), Prigogine and others extended the formalism of thermostatics to link the rate of entropy change to rates of the out-of-equilibrium processes (e.g., the Clausius–Duhem inequality).

From this modern angle, thermodynamics is a theory of irreversible processes, not just a theory of equilibrium states. (Kondepudi & Prigogine, Modern Thermodynamics: From Heat Engines to Dissipative Structures).

Therefore, modern thermodynamics is equipped with a formalism to calculate the rate of entropy changes due to irreversible processes (see e.g. On the Irreversible Production of Entropy by Tolman). Hence, thermodynamics describes macroscopic systems that vary slowly in time (slowly enough that we can consider a limited number of collective degrees of freedom, see e.g. section II of this paper for a contemporary point of view), not necessarily so slowly that everything is always at equilibrium.

Within thermodynamics, thermostatics deals with equilibrium states and transformations between them where time is not an explicit variable: thermostatics ignores the flows, i.e. the time derivatives of the macroscopic quantities such as energy, density, chemical fractions... and everything that happens during the evolution between the two equilibrium states.

As a final note, beware that terminology may differ a lot between different books, especially when it comes down to terms like "adiabatic" to indicate slow processes (so if you check any book, be sure of what they mean by certain key terms).

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A "non-equilibrium" system held steady was coined "thermostaedics" by Prof. Ralph J. Tykodi (now deceased)who was my advisor on my M.S. Thesis under the title of a book that he published called, "Thermodynamics of the Steady State" at Illinois Institute of Technology. Thermostaedics seems to me best because it covers any system as it approaches equilibrium slowly.

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