5 ms·

> entropy is the ability to extract useful work from a system https://www.damtp.cam.ac.uk/user/tong/statphys/jaynes.pdf https://www.damtp.cam.ac.uk/user/tong/s

by kgwgk 2y ago

> entropy is the ability to extract useful work from a system https://www.damtp.cam.ac.uk/user/tong/statphys/jaynes.pdf https://www.damtp.cam.ac.uk/user/tong/statphys/jaynes.pdf The amount of useful work that we can extract from any system depends - obviously and necessarily - on how much “subjective” information we have about its microstate, because that tells us which interactions will extract energy and which will not; this is not a paradox, but a platitude. If the entropy we ascribe to a macrostate did not represent some kind of human information about the underlying microstates, it could not perform its thermodynamic function of determining the amount of work that can be extracted reproducibly from that macrostate. […] the rules of thermodynamics are valid and correctly describe the measurements that it is possible to make by manipulating the macro variables within the set that we have chosen to use. This useful versatility - a direct result of and illustration of the “anthropomorphic” nature of entropy - would not be apparent to, and perhaps not believed by, someone who thought that entropy was, like energy, a physical property of the microstate. Edit: I’ve just noticed that the article discussed links to this paper, and quotes the first sentence above, and details the whifnium example given in the […] above.

tsimionescu 2y ago
I think this is a very weird thought experiment, and one that is either missing a lot of context or mostly just wrong. In particular, if two people had access to the same gas tank, and one knew that there were two types of argon and the other didn't, so they would compute different entropies, one of them would still be wrong about how much work could be extracted out of the system. If whifnium did exist, but it was completely unobtainable, then both physicists would still not be able to extract any work out of the system. If the one that didn't know about whifnium was given some amount of it without being told what it was, and instructed in how to use it, they would still see the same amount of work being done with it as the one who did know. They would just find out that they were wrong in their calculation of the entropy of the system, even if they still didn't know how or why. And of course, this also proves that the system had the same entropy even before humanity existed, and so the knowledge of the existence of whifnium is irrelevant to the entropy of the system. It of course affects our measurement of that entropy, and it affects the amount of work we can get that system to perform, but it changes nothing about the system itself and its entropy (unless of course you tautologically define entropy as the amount of work the experimenter/humanity can extract from the system).
- kgwgk 2y ago
  > unless of course you tautologically define entropy as the amount of work the experimenter/humanity can extract from the system Do you have a different definition? (By the way the entropy is the energy that _cannot_ be extracted as work.) The entropy of the system is a function of the particular choice of state variables - those that the experimenters can manipulate and use to extract work. It’s not a property of the system on its own. There is no “true” entropy anymore that there is a “true” set of state variables for the “true” macroscopic (incomplete) description of the system. If there was a true limiting value for the entropy it would be zero - corresponding to the case where the system is described using every microscopic variable and every degree of freedom could be manipulated.
  - tsimionescu 2y ago
    Yes, the more regular statistical mechanics theory of entropy doesn't make any reference to an observer, and definitely not to a human observer. In that definition, the entropy of a thermodynamic system is proportional to the amount of microstates (positions, types, momentum, etc. of individual particles) that would lead to the same macrostate (temperature, volume, pressure, etc.). It doesn't matter if an observer is aware of any of this, it's an objective property of the system. Now sure, you could choose to describe a gas (or any other system) in other terms and compute a different value for entropy with the same generalized definition. But you will not get different results from this operation - the second law of thermodynamics will still apply, and your system will be just as able or unable to produce work regardless of how you choose to represent it. You won't get better efficiency out of an engine by choosing to measure something other than the temperature/volume/pressure of the gases involved, for example. Even if you described the system in terms its specific microstate, and thus by the definition above your computed entropy would be the minimum possible, you still wouldn't be able to do anything that a more regular model couldn't do. Maxwell's demon is not a physically possible being/machine.
    - kgwgk 2y ago
      > the entropy of a thermodynamic system is proportional to the amount of microstates (positions, types, momentum, etc. of individual particles) that would lead to the same macrostate (temperature, volume, pressure, etc.). It doesn't matter if an observer is aware of any of this, it's an objective property of the system. The meaning of "would lead to the same macrostate" (and therefore the entropy) is not an "objective" property of the system (positions, types, momentum, etc. of individual particles). At least not in the way that the energy is an "objective" property of the system. The entropy is an "objective" property of the pair formed by the system (which can be described by a microstate) and some particular way of defining macrostates for that system. 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 that description is external to the physical system itself). Of course, if you define "system" as "the underlying microscopical system plus this thermodynamical system description that takes into account some derived state variables only" the situation is not the same as if you define "system" as "the underlying microscopical system alone".

by kgwgk 2y ago

tsimionescu 2y ago

I think this is a very weird thought experiment, and one that is either missing a lot of context or mostly just wrong. In particular, if two people had access to the same gas tank, and one knew that there were two types of argon and the other didn't, so they would compute different entropies, one of them would still be wrong about how much work could be extracted out of the system. If whifnium did exist, but it was completely unobtainable, then both physicists would still not be able to extract any work out of the system. If the one that didn't know about whifnium was given some amount of it without being told what it was, and instructed in how to use it, they would still see the same amount of work being done with it as the one who did know. They would just find out that they were wrong in their calculation of the entropy of the system, even if they still didn't know how or why. And of course, this also proves that the system had the same entropy even before humanity existed, and so the knowledge of the existence of whifnium is irrelevant to the entropy of the system. It of course affects our measurement of that entropy, and it affects the amount of work we can get that system to perform, but it changes nothing about the system itself and its entropy (unless of course you tautologically define entropy as the amount of work the experimenter/humanity can extract from the system).

kgwgk 2y ago
> unless of course you tautologically define entropy as the amount of work the experimenter/humanity can extract from the system Do you have a different definition? (By the way the entropy is the energy that _cannot_ be extracted as work.) The entropy of the system is a function of the particular choice of state variables - those that the experimenters can manipulate and use to extract work. It’s not a property of the system on its own. There is no “true” entropy anymore that there is a “true” set of state variables for the “true” macroscopic (incomplete) description of the system. If there was a true limiting value for the entropy it would be zero - corresponding to the case where the system is described using every microscopic variable and every degree of freedom could be manipulated.
- tsimionescu 2y ago
  Yes, the more regular statistical mechanics theory of entropy doesn't make any reference to an observer, and definitely not to a human observer. In that definition, the entropy of a thermodynamic system is proportional to the amount of microstates (positions, types, momentum, etc. of individual particles) that would lead to the same macrostate (temperature, volume, pressure, etc.). It doesn't matter if an observer is aware of any of this, it's an objective property of the system. Now sure, you could choose to describe a gas (or any other system) in other terms and compute a different value for entropy with the same generalized definition. But you will not get different results from this operation - the second law of thermodynamics will still apply, and your system will be just as able or unable to produce work regardless of how you choose to represent it. You won't get better efficiency out of an engine by choosing to measure something other than the temperature/volume/pressure of the gases involved, for example. Even if you described the system in terms its specific microstate, and thus by the definition above your computed entropy would be the minimum possible, you still wouldn't be able to do anything that a more regular model couldn't do. Maxwell's demon is not a physically possible being/machine.
  - kgwgk 2y ago
    > the entropy of a thermodynamic system is proportional to the amount of microstates (positions, types, momentum, etc. of individual particles) that would lead to the same macrostate (temperature, volume, pressure, etc.). It doesn't matter if an observer is aware of any of this, it's an objective property of the system. The meaning of "would lead to the same macrostate" (and therefore the entropy) is not an "objective" property of the system (positions, types, momentum, etc. of individual particles). At least not in the way that the energy is an "objective" property of the system. The entropy is an "objective" property of the pair formed by the system (which can be described by a microstate) and some particular way of defining macrostates for that system. 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 that description is external to the physical system itself). Of course, if you define "system" as "the underlying microscopical system plus this thermodynamical system description that takes into account some derived state variables only" the situation is not the same as if you define "system" as "the underlying microscopical system alone".