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What is entropy? A measure of just how little we know

quantamagazine.org

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Re: What is entropy? A measure of just how little we know

#161

Post by tsimionescu »

kgwgk wrote: post #154
tsimionescu wrote: post #151

Earlier quoted context omitted.

I would say that any state that we can't measure is not a physical state. So if we can only measure, even in theory, a system up to precision dx, then the system being in state a means that some quantity is x±dx. If the rules say that the system evolves from states where y>=x to state A, and from states where y This is similar to quantum measurement: when we see that the particle was here and not there, we don't lear…

> I would say that any state that we can't measure is not a physical state. Ok, so if I understand correctly for you microstates are not physical states and it doesn't make sense to even consider that at any given moment the system may be in a particular microstate. That's one way to look at things but the usual starting point for statistical mechanics is quite different.

That would be a bit too strong a wording. I would just say that certain theoretical microstates (ones that assume that position and velocity and so on are real properties that particles possess and can be specified by infinitely precise numbers) are not in fact physically distinguishable. Physical microstates do exist, but they are subject to the Heisenberg limit, and possibly other, less well defined/determined precision limits.

Beyond some level of precision, the world becomes fundamentally non-deterministic again, just like it appears in the macro state description.

Re: What is entropy? A measure of just how little we know

#162

Post by kgwgk »

tsimionescu wrote: post #160
kgwgk wrote: post #156

Earlier quoted context omitted.

> I understand that's what they mean, but this is the part that I think is either trivial or wrong. That is, depending on your choice you'll of course get different values, but it won't change anything about the system. It's basically like choosing to measure speed in meters per second or in furlongs per fortnight, or choosing the coordinate system and reference frame: you get radically different values, but relative…

> However when you put together one volume of helium and a one volume of argon the entropy calculated under choice (a) doesn't change but the entropy calculated under choice (b) does increase. We're not calculating the same thing in different units: we're calculating different things. There is no change of units that makes a quantity change and also remain constant! Agreed, this is not like a coordinate transform at…

It will predict how other certain experiments with the combined gas will behave. That's what people mean when they say that the entropy is not an "objective" property of a physical system: that it depends on how we choose to describe that physical system - and what experiments we can perform acting on that description.

Re: What is entropy? A measure of just how little we know

#163

Post by rwoerz »

lysecret wrote: post #136
rwoerz wrote: post #121

I don't get the example under "What is entropy?". This works only under the assumption that reality (phase space in particular) is somehow "pixelated". If reality is continuous, 9 particles that are clumped together can already be in uncountalbly many states.

Isn't that the whole point of quantum theory, it's quantized? Or did I get that wrong?

AFAIK only certain dimensions are quantized in quantum physics, e.g., energy states. Position is none of them.

Re: What is entropy? A measure of just how little we know

#164

Post by datavirtue »

hnfong wrote: post #134
swyx wrote: post #129

Earlier quoted context omitted.

why is it exciting at all? it is the most depressing concept i have ever heard.

What's depressing about it?

They are hung up on determinism and absolutes. In that world-view entropy is literally the devil.

Re: What is entropy? A measure of just how little we know

#165

Post by tsimionescu »

kgwgk wrote: post #162
tsimionescu wrote: post #160

Earlier quoted context omitted.

> However when you put together one volume of helium and a one volume of argon the entropy calculated under choice (a) doesn't change but the entropy calculated under choice (b) does increase. We're not calculating the same thing in different units: we're calculating different things. There is no change of units that makes a quantity change and also remain constant! Agreed, this is not like a coordinate transform at…

It will predict how other certain experiments with the combined gas will behave. That's what people mean when they say that the entropy is not an "objective" property of a physical system: that it depends on how we choose to describe that physical system - and what experiments we can perform acting on that description.

What would be an example of such an experiment?

By my understanding, even if we have no idea what gas we have, if we put it into a calorimeter and measure the amount of heat we need to transfer to it to change its temperature to some value, we will get a value that will be different for a gas made up of only argon versus one that contains both neon and argon. Doesn't this show that there is some objective definition of the entropy of the gas that doesn't care about an observer's knowledge of it?

Re: What is entropy? A measure of just how little we know

#166

Post by kgwgk »

tsimionescu wrote: post #165
kgwgk wrote: post #162

Earlier quoted context omitted.

It will predict how other certain experiments with the combined gas will behave. That's what people mean when they say that the entropy is not an "objective" property of a physical system: that it depends on how we choose to describe that physical system - and what experiments we can perform acting on that description.

What would be an example of such an experiment? By my understanding, even if we have no idea what gas we have, if we put it into a calorimeter and measure the amount of heat we need to transfer to it to change its temperature to some value, we will get a value that will be different for a gas made up of only argon versus one that contains both neon and argon. Doesn't this show that there is some objective definition…

Actually the molar heat capacity for neon, or argon, or a mixture thereof, is the same. These are monotomic ideal gases as far as your calorimeter measurements can see.

If the number of particles is the same you’ll need the same heat to increase the temperature by some amount and the entropy increase will be the same. Of course you could do other things to find out what it is, like weighing the container or reading the label.

Re: What is entropy? A measure of just how little we know

#167

Post by tsimionescu »

kgwgk wrote: post #166
tsimionescu wrote: post #165

Earlier quoted context omitted.

What would be an example of such an experiment? By my understanding, even if we have no idea what gas we have, if we put it into a calorimeter and measure the amount of heat we need to transfer to it to change its temperature to some value, we will get a value that will be different for a gas made up of only argon versus one that contains both neon and argon. Doesn't this show that there is some objective definition…

Actually the molar heat capacity for neon, or argon, or a mixture thereof, is the same. These are monotomic ideal gases as far as your calorimeter measurements can see. If the number of particles is the same you’ll need the same heat to increase the temperature by some amount and the entropy increase will be the same. Of course you could do other things to find out what it is, like weighing the container or reading t…

No, they are not. The entropy of an ideal monatomic gas depends on the mass of its atoms (see the Sackur–Tetrode equation). And a gas mix is not an ideal monatomic gas; its entropy increases at the same temperature and volume compared to an equal volume divided between the two gases.

Also, entropy is not the same thing as heat capacity. It's true that I didn't describe the entropy measurement process very well, so I may have been ambiguous, but they are not the same quantity.

Re: What is entropy? A measure of just how little we know

#168

Post by kgwgk »

tsimionescu wrote: post #167
kgwgk wrote: post #166

Earlier quoted context omitted.

Actually the molar heat capacity for neon, or argon, or a mixture thereof, is the same. These are monotomic ideal gases as far as your calorimeter measurements can see. If the number of particles is the same you’ll need the same heat to increase the temperature by some amount and the entropy increase will be the same. Of course you could do other things to find out what it is, like weighing the container or reading t…

No, they are not. The entropy of an ideal monatomic gas depends on the mass of its atoms (see the Sackur–Tetrode equation). And a gas mix is not an ideal monatomic gas; its entropy increases at the same temperature and volume compared to an equal volume divided between the two gases. Also, entropy is not the same thing as heat capacity. It's true that I didn't describe the entropy measurement process very well, so I…

I'll leave the discussion here but let me remind you that you talked (indirectly) about changes in entropy and not about absolute entropies: "if we put it into a calorimeter and measure the amount of heat we need to transfer to it to change its temperature to some value".

Note as well that the mass dependence in that equation for the entropy is just an additive term. The absolute value of the entropy may be different but the change in entropy is the same when you heat a 1l container of helium or neon or a mixture of them from 300K to 301K. That's 0.0406 moles of gas. The heat flow is 0.506 joules. The change in entropy is approximately 0.0017 J/K.

> And a gas mix is not an ideal monatomic gas; its entropy increases at the same temperature and volume compared to an equal volume divided between the two gases.

A mix of ideal gases is an ideal gas and its heat capacity is the weighted average of the heat capacities (trivially equal to the heat capacity of the components when it's the same). The change of entropy when you heat one, or the other, or the mix, will be the same (because you're calculating exactly the same integral of the same heat flow).

The difference in absolute value is irrelevant when we are discussing changes in entropy and measurements of the amount of heat needed to increase the temperature and whether you "will get a value that will be different for a gas made up of only argon versus one that contains both neon and argon".

Re: What is entropy? A measure of just how little we know

#169

Post by ziofill »

bee_rider wrote: post #62
ziofill wrote: post #56

Very nice article. There’s an alternative way of thinking of the Gibbs paradox, which is to attach labels to the particles. This naturally makes them distinguishable and increases the total number of possible configurations, and with it the maximum value of the entropy.

Attaching labels to the particles would make them fundamentally different types of particles, right? So it doesn’t seem that surprising that a system with different types of particles would be different.

Yes but that’s the same as gathering new information about them
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