5 ms·

> The more possible configurations there are, the greater the entropy. And this explains the second law: given a set of measurement values, the more states ther

by effie 4y ago

> The more possible configurations there are, the greater the entropy. And this explains the second law: given a set of measurement values, the more states there are which produce those values, the more likely we are, all else being equal, to observe those values. And so a closed system will evolve by pure chance into a state where the entropy is maximized simply because you are more likely to observe values corresponding to greater numbers of underlying states. This is an argument for observing high entropy macrostates at any time, assuming all microstates are equally probable. But not for evolution in time that makes entropy higher in the future, or at least non-smaller in the future. You assume the closed system evolves its microstate in time "by pure chance", i.e. any microstate is equally probable as the next microstate, which ignores many constraints there are due to physics laws like conservation of phase volume or energy. This probabilistic argument could be applied to past just as well as the future. But observations show entropy of an isolated system is lower in the past than in the present. So your argument does not really derive all aspects of 2nd law.

lisper 4y ago
> But not for evolution in time that makes entropy higher in the future, or at least non-smaller in the future. Well, obviously the system is subject to the constraints of its dynamics. It's not just picking a new microstate at random at each instant in time. It can only evolve to states that are accessible from its current state according to its dynamics. But given that set of accessible microstates, you are more likely to get a macrostate corresponding to a larger number of microstates than a smaller number. The reason entropy was lower in the past is that the universe started out in a low-entropy state. The reason for that is still a mystery.
- effie 4y ago
  > But given that set of accessible microstates, you are more likely to get a macrostate corresponding to a larger number of microstates than a smaller number. This is due to mixing in phase space, which is plausible for many particle systems. However, it works in both directions of the parameter t. The only way to derive 2nd law including its time asymmetry (which is the major point of 2nd law) is to restrict considerations to those microscopic processes that are compatible with macroscopic processes that systematically lead to the same final state. This means we consider only subset of all microscopically possible processes. E.g. Jaynes selects those macroscopic processes that bring one macrostate A, via some irreversible evolution, to another macrostate B, repeatedly. Then, assuming this reliability of the resulting state, he derives non-decrease of entropy from maximum entropy principle and Hamiltonian statistical physics. If we didn't assume this restriction and allowed all mechanically possible processes, entropy could both increase and decrease. > The reason entropy was lower in the past is that the universe started out in a low-entropy state. The reason for that is still a mystery. This often repeated idea is in vein with Clausius' ostentatious statements on energy and entropy of the Universe, which have been out of place and plagued discussions of thermodynamics with needless mystical assumptions ever since he wrote them. There is no evidence for them, as there are no reliable measurements of entropy of the Universe. There is no need for them, as there are no good reasons to believe Universe has defined entropy at all. Thermodynamics, including 2nd law, is about finite sized systems free of strong gravity effects. It does not extrapolate easily beyond compact systems like planets/stars to ever bigger systems. There is no Universe in it anywhere. 2nd law that we see in daily life or a lab is not a statement about entropy of Universe being lower in the past, nor does it hang on such an assumption. It is (in one of its variants) the statement that a finite isolated system can change its macrostate to some other final macrostate, but this final macrostate is of higher or same entropy, so in real process entropy can't decrease.
  - lisper 4y ago
    > The only way to derive 2nd law including its time asymmetry... I don't think that's true, though I'm not sure I understand what you mean by "those microscopic processes that are compatible with macroscopic processes that systematically lead to the same final state". (The same as what? The same in what sense?) The reason you can't unscramble an egg is not because there is anything fundamentally irreversible in the laws of physics, it's because the time-evolution of the scrambling egg is governed not only by the motion of the whisk but also by the random thermalized motion of the constituent particles. To unscramble the egg you would need not only to precisely reverse the motion of the whisk, but also all of the thermal velocities of the constituent particles. The latter might be possible in principle (though not in practice) in a classical world, but throw in quantum mechanics and it's not possible even in principle. So the second law happens simply because the dynamics of non-trivial systems (like eggs) are chaotic, and quantum mechanics always throws in some randomness at the lowest levels. And yes, quantum mechanics is also time-reversible. If you want to quibble about that, read this first: https://blog.rongarret.info/2014/10/parallel-universes-and-arrow-of-time.html https://blog.rongarret.info/2014/10/parallel-universes-and-a... > There is no evidence for them If you believe that the 2nd law is universal (and I see no reason to doubt it) then the inescapable conclusion is that the further back you go, the lower the entropy of the universe was, reaching a global minimum at inception.
    - effie 4y ago
      > I'm not sure I understand what you mean by "those microscopic processes that are compatible with macroscopic processes that systematically lead to the same final state". (The same as what? The same in what sense?) In the formulation of 2nd law for adiabatically isolated systems, there is the initial equilibrium macrostate A, and the different equilibrium macrostate B that the system gets into eventually after the intervention, where either some constraint is released, or some macroscopic work is done. 2nd law states that if the same intervention in A results in B reliably, then S_B >= S_A. This statement can be derived from mechanics and maximum entropy principle only under the assumption that B is a reliable result of intervention in A (always or with close to 1 probability). This is more than mechanics or logic can provide, and it means we have a restriction on the allowed set of microscopic processes considered. It is not possible to derive 2nd law from mechanics or logic for all microscopic processes. Some microscopic processes bring the state B to state A, and those break 2nd law.

by effie 4y ago

lisper 4y ago

> But not for evolution in time that makes entropy higher in the future, or at least non-smaller in the future. Well, obviously the system is subject to the constraints of its dynamics. It's not just picking a new microstate at random at each instant in time. It can only evolve to states that are accessible from its current state according to its dynamics. But given that set of accessible microstates, you are more likely to get a macrostate corresponding to a larger number of microstates than a smaller number. The reason entropy was lower in the past is that the universe started out in a low-entropy state. The reason for that is still a mystery.

effie 4y ago
> But given that set of accessible microstates, you are more likely to get a macrostate corresponding to a larger number of microstates than a smaller number. This is due to mixing in phase space, which is plausible for many particle systems. However, it works in both directions of the parameter t. The only way to derive 2nd law including its time asymmetry (which is the major point of 2nd law) is to restrict considerations to those microscopic processes that are compatible with macroscopic processes that systematically lead to the same final state. This means we consider only subset of all microscopically possible processes. E.g. Jaynes selects those macroscopic processes that bring one macrostate A, via some irreversible evolution, to another macrostate B, repeatedly. Then, assuming this reliability of the resulting state, he derives non-decrease of entropy from maximum entropy principle and Hamiltonian statistical physics. If we didn't assume this restriction and allowed all mechanically possible processes, entropy could both increase and decrease. > The reason entropy was lower in the past is that the universe started out in a low-entropy state. The reason for that is still a mystery. This often repeated idea is in vein with Clausius' ostentatious statements on energy and entropy of the Universe, which have been out of place and plagued discussions of thermodynamics with needless mystical assumptions ever since he wrote them. There is no evidence for them, as there are no reliable measurements of entropy of the Universe. There is no need for them, as there are no good reasons to believe Universe has defined entropy at all. Thermodynamics, including 2nd law, is about finite sized systems free of strong gravity effects. It does not extrapolate easily beyond compact systems like planets/stars to ever bigger systems. There is no Universe in it anywhere. 2nd law that we see in daily life or a lab is not a statement about entropy of Universe being lower in the past, nor does it hang on such an assumption. It is (in one of its variants) the statement that a finite isolated system can change its macrostate to some other final macrostate, but this final macrostate is of higher or same entropy, so in real process entropy can't decrease.
- lisper 4y ago
  > The only way to derive 2nd law including its time asymmetry... I don't think that's true, though I'm not sure I understand what you mean by "those microscopic processes that are compatible with macroscopic processes that systematically lead to the same final state". (The same as what? The same in what sense?) The reason you can't unscramble an egg is not because there is anything fundamentally irreversible in the laws of physics, it's because the time-evolution of the scrambling egg is governed not only by the motion of the whisk but also by the random thermalized motion of the constituent particles. To unscramble the egg you would need not only to precisely reverse the motion of the whisk, but also all of the thermal velocities of the constituent particles. The latter might be possible in principle (though not in practice) in a classical world, but throw in quantum mechanics and it's not possible even in principle. So the second law happens simply because the dynamics of non-trivial systems (like eggs) are chaotic, and quantum mechanics always throws in some randomness at the lowest levels. And yes, quantum mechanics is also time-reversible. If you want to quibble about that, read this first: https://blog.rongarret.info/2014/10/parallel-universes-and-arrow-of-time.html https://blog.rongarret.info/2014/10/parallel-universes-and-a... > There is no evidence for them If you believe that the 2nd law is universal (and I see no reason to doubt it) then the inescapable conclusion is that the further back you go, the lower the entropy of the universe was, reaching a global minimum at inception.
  - effie 4y ago
    > I'm not sure I understand what you mean by "those microscopic processes that are compatible with macroscopic processes that systematically lead to the same final state". (The same as what? The same in what sense?) In the formulation of 2nd law for adiabatically isolated systems, there is the initial equilibrium macrostate A, and the different equilibrium macrostate B that the system gets into eventually after the intervention, where either some constraint is released, or some macroscopic work is done. 2nd law states that if the same intervention in A results in B reliably, then S_B >= S_A. This statement can be derived from mechanics and maximum entropy principle only under the assumption that B is a reliable result of intervention in A (always or with close to 1 probability). This is more than mechanics or logic can provide, and it means we have a restriction on the allowed set of microscopic processes considered. It is not possible to derive 2nd law from mechanics or logic for all microscopic processes. Some microscopic processes bring the state B to state A, and those break 2nd law.