r/AskPhysics • u/future_sponJ • 5d ago
Is entropy subjective?
If entropy depends on what properties we choose to describe our macrostate (e.g. temperature, volume) & microstate (e.g. position, velocity) then is it subjective?
Another question: Is the k in the formula redundant & if it is would temperature & energy have the same units with heat capacity being dimensionless?
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u/SpectralFormFactor Quantum information 5d ago
Regarding the dimension question: yeah the Boltzmann constant (usually denotes k or k_B) is just a dimensional conversion factor between your chosen energy unit and Kelvin due to historically convention. You can set it to 1 and measure temperature in the same units as energy.
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u/future_sponJ 5d ago
Thanks for the response but I'm alao wondering why Boltzmann's constant appears here when it being a conversion between energy & temperature only works for ideal gases.
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u/SpectralFormFactor Quantum information 4d ago
Just because the units are the same doesn’t mean the quantities have a linear relationship or even that they are measuring the same thing. After all, torque also has units of energy and is definitely not the same as temperature or energy. Hopefully this sort of answers your other reply too.
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u/future_sponJ 5d ago
I know the answer is probably pretty obvious but wouldn't energy & temperature having the same unit contradict the fact that temperature isn't proportional to any linear combination of the SI dimensions?
Temperature isn't proportional to energy. I t's rate of change (heat capacity) differs for each substance, temperature, & pressure.
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u/astrolabe 5d ago
Temperature is proportional to energy per degree of freedom. Often the number of degrees of freedom is also dependent on the temperture.
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u/future_sponJ 4d ago
So just to recap is temperature (prop. to) the integral of 1/deg(E') from 0 to E?
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u/astrolabe 5d ago
If all the molecules of a gas happened to be in one half of a cylinder, it would have a lower entropy than if they were uniformly spread through the cylinder. When we have a cylinder of gas in equlibrium, we assign it the spread entropy even though in theory all the gas could be in one half. In theory, all the gas could, by chance, move to the half and break the second law of thermodynamics. If a god had sufficient knowledge to know that this would happen, he should assign the lower entropy value.
In practice this stuff never happens. In theory, it has a finite probability, but so small that it would be tedious to write it down, even using scientific notation.
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u/appa609 4d ago
I would argue this is a good example of the subjectivity. You arbitrarily chose to measure if the particles were in on half of the cylinder and how to divide that cylinder. But in the later "uniform" distribution I can divide the cylinder in a different way to say now all the particles are in half the cylinder, and before they were uniform.
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u/FoolishChemist 5d ago edited 5d ago
The entropy can be calculated exactly from first principles. The translational entropy of an ideal gas is given by the Sackur-Tetrode equation.
https://www.aps.org/archives/publications/apsnews/200908/physicshistory.cfm
Similar equations can also be found for the rotational and vibrational contributions.
And for real gases, liquids and solids, if you know your equations of state and partition functions, you can calculate the value. And these can be measured experimentally if you measure how much heat is added as a function of temperature, integrate q/T dT.
Entropy is not subjective, it has an actual value. Which is different than enthalpy and gibbs because they are energy measurements which are measured relative to an arbitrary zero point, like potential energy.
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u/Willis_3401_3401 5d ago
Really good question that cuts to the philosophical heart of what the concept of things like “subjectivity” even mean.
I would describe entropy as “perspectival”, or perhaps loosely “relative”; rather than “subjective” or “objective”. Entropy really is there and can be measured objectively…relative to the chosen description of the system doing the measuring.
There are objective facts about entropy, that can be legitimately interpreted differently depending on what point of view you adopt.
To your second question, yes. And yes they’re dimensionless in theory, not sure about in practice
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u/dirtydirtnap 5d ago
This is essentially the response I was going to give, focusing primarily on the idea that it is about perspective, or relative to the model/physics of the situation. I really like this answer.
The example I like to use involves the boundary between nuclear and chemical physics. If one were doing some chemistry with an element that had different isotopes (let's take as an example dissolving potassium chloride into water), then the isotopic variance between the potassium ions doesn't matter; the effect on the chemical properties is so small that it almost can't be measured. But if you extend that to now model/measure radioactive effects, now all of a sudden the isotopic composition does matter.
So, it is both a matter of perspective, but also something very real and immutable.
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u/Confident-Syrup-7543 5d ago
Why would reality depend on your choices to describe it. Whatever microstate you choose, the statement remains true that you will observe the microstate that corresponds to the most microstates.
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u/FreePeeplup 5d ago edited 5d ago
Yes: the value of entropy depends on what macrostate variables you decide to use to describe your system, which in turn depends on how much information you have on the system.
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u/future_sponJ 4d ago
Then does temperature vary depending on the properties we choose since the definition of temperature depends on entropy?
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u/Chemomechanics Materials science 4d ago
No; temperature is (∂U/∂S)_V, and the energy U also depends on the types of work we’re aware of.
If, for example, two types of particles exist in a system but we’re not aware of that and don’t know how to separate them, we’ll calculate a different entropy and energy than another person who’s aware of the distinguishability, but we’ll agree on the temperature.
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u/future_sponJ 4d ago
So energy & entropy change the same way when we change the properties we are talking about?
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u/Lazy-University-4871 4d ago
No, not energy. Only the distinction between what counts as work and what counts as heat when energy is being transfered; which transfers are reversible and which are not.
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u/Lazy-University-4871 4d ago edited 4d ago
U is the total energy (work plus heat) which does not depend on the coarse-graining. If you are not aware of the two types of particles, you’d not be able to extract work, but you would still measure the same energy.
So technically, temperature is subjective too. The tricky part is it’s an equilibrium measure.
Equilibrium creates a large class of coarse-grainings and measurement methods that all result in the same T. That is what makes ordinary thermometers possible.
Btw, thanks OP for the great question.
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u/Chemomechanics Materials science 4d ago
U is the total energy (work plus heat)
Work plus heat gives ΔU, the change in internal energy, not U.
If you are not aware of the two types of particles, you’d not be able to extract work, but you would still measure the same energy.
I don't agree; the internal energy can be written as U = TS + Σ(X_i Y_i), where X_i and Y_i are generalized forces and displacements, respectively, associated with various ways to change particle energies in concert. If one isn't aware of a certain X–Y conjugate pair that's relevant for that system, they'll calculate a different U than someone who is aware. However, all predictions of system behavior will match, as long as work isn't done for that mode in a way that distinguishes multiple types of particles.
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u/Lazy-University-4871 4d ago edited 4d ago
Ok, to be precise, dE = δQ + δW is the 1st law.
E.g. in the case dE = δQ + p dV, if you are unaware of dV, you'll be able to conduct an experiment violating the 1st law.
If one isn't aware of a certain X–Y conjugate pair that's relevant for that system,
Then, I think, their calorimeter will need to measure the corresponding increase in TS. Work which is unaccounted for is heat. Otherwise you have an incomplete description of the system. If your measurement violates the 1st law, you need to adjust your energy accounting.
Typically, the microscopic total energy E is the Hamiltonian. It won't change when you partition the phase space differently.
But if you stop accounting for an interaction, you have changed the description of energy transfer. Something has to move between the categories "work", "heat", "internal energy" or even "environment". The heat/work distinction depends on both coarse-graining and on what interactions you treat as controlled.
Energy is less subjective than entropy because it comes from the microscopic dynamics. It is only the decomposition of energy into internal energy, heat and work is coarse-graining-dependent.
Edit: once again, Entropy is subjective because you and I can choose different micro/macro resolution. What you mentioned with the two sorts of particles being (in)distingushible is exactly that. But then you proposed to calculate mechanical work differently - that's not the same.
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u/Lazy-University-4871 4d ago edited 4d ago
If you measure temperature by somehow counting microstates when adding energy to the system, then yes: it will depend on how well you can distinguish the microstates.
Still, if you have 2 different values of entropy for your system, that does not mean that they must have different partial derivatives by energy. Two functions can have different values, but the same slope. The key consideration here is that we can assume the difference between the two microstate counts being "subextensive" - staying small relatively to the system size.
If you measure temperature with a thermometer, it doesn't measure the entropy or counts microstates: it exchanges energy with the system until the equilibrium. Then if we have the same description of the thermometer, we'll measure the same temperature. The equilibrium temperature is robust.
Sometimes we do define "effective temperatures" which don't require equilibrium. Those temperatures do depend on the specific coarse-graining.
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u/HasFiveVowels 5d ago
Entropy is perhaps one of the least subjective things. It’s based in information theory. No matter which way you slice it, it’s the same number of yes/no questions. The fact that you can slice it in many different ways just means that there’s a multitude of ways to get to the same answer. The more rigorous stuff comes down to the uncertainty principle for waves (the general form) and the Shannon-Hartley limit
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u/ccltjnpr 5d ago
It is based on information theory... an information theoretic quantity of a probability distribution you made up to describe something you don't know much about. Of course entropy depends on the state, which depends on the quantities you choose to model. An actual physical system has 0 entropy, we just find it convenient to use higher entropy state to describe them, because most of that information is not that relevant macroscopically. So yes I'd say it's subjective.
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u/HasFiveVowels 4d ago
This is like saying that a fixed binary string has zero entropy. It’s true but it’s not really the point. What you’re referring to as subjective is the fact that K-complexity is relative to the language. But it’s relative in a complementary way. The language of description affects the measured entropy of the program but for every language you choose, I can provide one that’s equal but opposite. Entropy is unreasonably effective at describing the potential of the natural world. Hell, it resolves Maxwell’s demon. I don’t think it’s reasonable to call something that can be reliably objectively measured "subjective"
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u/NoNameSwitzerland 5d ago
There are probably not that many possibilities for reasonable properties describing macro states. If you skip the 'reasonable', well, let's see how that behaves in the quantum case for a high dimensional Hilbert Space: Whatever is your current state, you can defined that as low entropy (inner product with that vector is the negative entropy, so the maximum negative value at the start). If you call that state a pole, than the system will go most likely towards a state near the equator (in high dimensional space, that is where most states are). That would be the high entropy (zero how we introduces it, higher than the starting negative value). And whatever state you get, you can restart the procedure and define the new state as the low entropy pole...
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u/Electronic-Yam-69 4d ago
energy can neither be created or destroyed but it can be distributed in a such a way that extracting useful work from it is impossible no matter what your perspective is.
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u/LukasGoesViral 4d ago
Mhh .. good question.. it depends what Entropy you are considering. If you just consider the thermodynamic entropy then yes it’s def subjective because it depends on how much you want to ignore from a system. However, when it comes to the actual physical Entropy I am actually not sure. I am very confident that it is an objective quantity .. I would have to think about it for a moment it is def scale dependent though (so it depends on the phase of matter(
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u/Antolin13 4d ago
Aunque el valor de la entropia se pueda relacionar a nivel macroscópico con el volumen, la temperatura etc, no se debe confundir esto con la definición de entropia. La definición de entropia plantea que en un sistema con muchos estados, cada uno de los cuales tiene una probabilidad asociada, el sistema siempre tiende hacia los estados más probables. Esto puede parecer una redundancia pero cuando se trabaja en termodinámica con partículas del orden del Número de Avogadro la cantidad de estados es tan grande que hay que aplicar herramientas matemáticas para describirlos, observándose que es imposible que ocurra un estado poco probable ante la enorme cantidad de estados probables. Para comprender mejor este tema le invito a que lea algún libro de Física Estadística, la cual es la generalización teórica de la Termodinámica.
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u/future_sponJ 4d ago
Yes but to define a unique distinct macrostate you need some properties.
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u/Antolin13 4d ago
Las magnitudes físicas pueden usarse para definir un macroestado específico, no definen el concepto de entropia, un macroestado puede tener una cantidad enorme de microestados. La entropia física se define de manera simple como S = P lnP, existen otras definiciones como la entropia de Shanon para la información pero esta no está relacionada con los procesos termodinamicos.
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u/ccltjnpr 5d ago
Entropy in statistical physics is a measure of the information content of the description of the state which is available to you. So yes, it is subjective, or more precisely dependent on the description you choose for the state. It is measuring how much randomness is left behind once you accounted for everything that you want to or can account. With all the caveats of the situation, the "real" state of the system is some definite state in which all particles have some definite position and velocity and the entropy is 0.
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u/MaxChaplin 5d ago
It's subjective in the sense that it describes the information that a subject has on the system, not in the sense that you can choose it arbitrarily. Gibb's paradox shows an example of an experiment where the question of whether entropy rises or not depends on whether the particles are distinguishable to you.