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> Our direction of time is defined by the observation that entropy (or "chaoticness") always increases with time. If you mix orange juice with water, you will n

by effie 11y ago

> Our direction of time is defined by the observation that entropy (or "chaoticness") always increases with time. If you mix orange juice with water, you will not see the result unmix itself again, even though the interactions between the individual molecules are perfectly reversible. Entropy does not always increase in time, because entropy is rarely a function of time. The most common meaning of the word is a thermodynamic quantity that is not, in general, defined in non-equilibrium states. It is a function of state variables rather than time. What people are talking about when they say "entropy increases in time" is actually some variant of minus Boltzmann H-function. This kind of resembles thermodynamic entropy, but is a distinct and less general concept. There are processes where entropy gets higher but "entropy" (minus Boltzmann H-function) get lower. If you mix oil and water, you will see the result does unmix itself again. Does this mean entropy decreased and time direction got reversed? Nah. It is not even clear how to define entropy of the system in between, since it is in highly non-equilibrium state.

trhway 11y ago
>If you mix oil and water, you will see the result does unmix itself again. Does this mean entropy decreased and time direction got reversed? Nah. Moving an object to higher gravitational potential decreases the entropy of the system (and thus requires work, unsurprisingly). Mixing oil into water means you displace some volume of water which were closer to Earth with oil bubbles (which are lighter than equivalent volume of water) while you force the displaced water volume higher/further from Earth. Thus by mixing lighter oil with heavier water you decrease the entropy of the gravitational system consisting of the oil, water and Earth. Left to its own devices, the system evolves along the entropy increasing gradient - heavy water goes down displacing lighter oil up, thus decreasing the gravitational potential of the system (the friction during that "unmixing" is the work of the gravitational force that ultimately results in the heat that is lost away into the environment).
- effie 11y ago
  When the fluids are mixed by a spoon, surely work has been done by the stirring spoon on the system and energy of the system increased. But this does not by itself imply entropy of the system increased. The reason is the system got to a non-equilibrium state which has no macroscopic thermodynamic description and no unique way to assign entropy and detect its changes.
  - trhway 11y ago
    >But this does not by itself imply entropy of the system increased. doesn't matter what way it got there, entropy of the gravitational system oil-water-Earth is lower and the gravitational potential is higher when oil bubbles are inside the water when compared with the same system in the state when all oil is on top of the water. Thus system naturally moves from the former state to the latter, from lower entropy to the higher, from higher gravitational potential to the lower.
    - effie 11y ago
      Of course, gravitational potential energy of the system is higher when the oil is scattered temporarily in the water, because the water is higher than it would be in equilibrium state. However, I do not see how this has anything to do with the concept of entropy. The non-equilibrium state cannot be easily assigned thermodynamic entropy, because there is no obvious thermodynamic state variable that could describe the state of mixed water and oil. If you know how to introduce such a variable and corresponding entropy, then please explain it.
      - trhway 11y ago
        >However, I do not see how this has anything to do with the concept of entropy. in short - entropy of the system with lower gravitational potential is higher (https://en.wikipedia.org/wiki/Entropic_gravity https://en.wikipedia.org/wiki/Entropic_gravity). When oil is mixed into water, the thermodynamic entropy "St,mix" of oil/water system is higher than "St,unmixed" while the entropy "Sg,mix" of the gravitational system of oil/water/Earth is lower when mixed than the "Sg,unmixed" of the unmixed case. In case of bad solubility, like oil in water, we have ["St,mix" - "St,unmixed" < "Sg,unmixed" - "Sg,mix"] and thus system on its own will evolve toward unmixed state.
        effie 11y ago
        Entropic explanation of gravity force is not an accepted physics theory. Regardless of whether it is right or not, the concept of entropy in common thermodynamics I was referring to above is different from that in entropic gravity. In thermodynamics, in contrast with theories of entropic forces, entropy is assigned only to states of thermodynamic equilibrium that can be achieved by exchanging heat reversibly. State that is not a state of mechanical equilibrium (such as state of accelerating bodies, unmixing water+oil) is not such a state.

by effie 11y ago

trhway 11y ago

>If you mix oil and water, you will see the result does unmix itself again. Does this mean entropy decreased and time direction got reversed? Nah. Moving an object to higher gravitational potential decreases the entropy of the system (and thus requires work, unsurprisingly). Mixing oil into water means you displace some volume of water which were closer to Earth with oil bubbles (which are lighter than equivalent volume of water) while you force the displaced water volume higher/further from Earth. Thus by mixing lighter oil with heavier water you decrease the entropy of the gravitational system consisting of the oil, water and Earth. Left to its own devices, the system evolves along the entropy increasing gradient - heavy water goes down displacing lighter oil up, thus decreasing the gravitational potential of the system (the friction during that "unmixing" is the work of the gravitational force that ultimately results in the heat that is lost away into the environment).

effie 11y ago
When the fluids are mixed by a spoon, surely work has been done by the stirring spoon on the system and energy of the system increased. But this does not by itself imply entropy of the system increased. The reason is the system got to a non-equilibrium state which has no macroscopic thermodynamic description and no unique way to assign entropy and detect its changes.
- trhway 11y ago
  >But this does not by itself imply entropy of the system increased. doesn't matter what way it got there, entropy of the gravitational system oil-water-Earth is lower and the gravitational potential is higher when oil bubbles are inside the water when compared with the same system in the state when all oil is on top of the water. Thus system naturally moves from the former state to the latter, from lower entropy to the higher, from higher gravitational potential to the lower.
  - effie 11y ago
    Of course, gravitational potential energy of the system is higher when the oil is scattered temporarily in the water, because the water is higher than it would be in equilibrium state. However, I do not see how this has anything to do with the concept of entropy. The non-equilibrium state cannot be easily assigned thermodynamic entropy, because there is no obvious thermodynamic state variable that could describe the state of mixed water and oil. If you know how to introduce such a variable and corresponding entropy, then please explain it.
    - trhway 11y ago
      >However, I do not see how this has anything to do with the concept of entropy. in short - entropy of the system with lower gravitational potential is higher (https://en.wikipedia.org/wiki/Entropic_gravity https://en.wikipedia.org/wiki/Entropic_gravity). When oil is mixed into water, the thermodynamic entropy "St,mix" of oil/water system is higher than "St,unmixed" while the entropy "Sg,mix" of the gravitational system of oil/water/Earth is lower when mixed than the "Sg,unmixed" of the unmixed case. In case of bad solubility, like oil in water, we have ["St,mix" - "St,unmixed" < "Sg,unmixed" - "Sg,mix"] and thus system on its own will evolve toward unmixed state.
      - effie 11y ago
        Entropic explanation of gravity force is not an accepted physics theory. Regardless of whether it is right or not, the concept of entropy in common thermodynamics I was referring to above is different from that in entropic gravity. In thermodynamics, in contrast with theories of entropic forces, entropy is assigned only to states of thermodynamic equilibrium that can be achieved by exchanging heat reversibly. State that is not a state of mechanical equilibrium (such as state of accelerating bodies, unmixing water+oil) is not such a state.