5 ms·

> 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 microscopi

by 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.
- lisper 4y ago
  > the initial equilibrium macrostate A, and the different equilibrium macrostate B that the system gets into eventually [emphasis added] Your use of "the" here, with the implication that there are two unique microstates A and B, is problematic. There is no such thing as "the" equilibrium microstate. A system at thermodynamic equilibrium is not static. (In fact, I think it is fair to say that the whole point of thermodynamics is to sweep vast numbers of the physical degrees of freedom of a system under the rug so that you can treat a system at equilibrium as if it were static even though it really isn't. It is frankly astonishing that this is even possible at all without losing any fidelity in terms of measurable outcomes.) > Some microscopic processes bring the state B to state A, and those break 2nd law. Yes, that's true. The second law is probabilistic. It is "possible" to break the second law in the same sense that it is "possible" for a baseball to quantum-mechanically tunnel through a catcher's mitt. You can do the math to figure the odds in both cases. In fact, actually going through this process is an informative exercise. It isn't difficult. There are some events whose probabilities are so low that the chance of them occurring anywhere in the universe before heat death is barely distinguishable from zero. The odds of actually observing such an event here on earth are vastly smaller still. Both macroscopic tunneling and 2nd law violations are events of this sort. Neither is categorically impossible, but (to put it mildly) it's pretty safe to bet against them nonetheless.
  - effie 4y ago
    You have missed my point. The formulation of 2nd law I'm talking about is stating something about all pairs of two MACROstates A,B, not MICROstates, such that B reliably succeeds A after intervention. This pair of MACROstates is not assumed unique, there are hugely many, but formulating the argument uses a single pair. (I'm not a native speaker so don't get distracted by possibly incorrect use of the definite article). The problem with your handwavy argument about macrostates with higher multiplicity is not due to 2nd law being a probabilistic claim. The problem is that it is not clear from that argument alone why it applies to future states, but it does not apply to the past states. To address that, another assumption is needed, such as the asymmetric relation between my macrostates A,B.

by lisper 4y ago

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.

lisper 4y ago
> the initial equilibrium macrostate A, and the different equilibrium macrostate B that the system gets into eventually [emphasis added] Your use of "the" here, with the implication that there are two unique microstates A and B, is problematic. There is no such thing as "the" equilibrium microstate. A system at thermodynamic equilibrium is not static. (In fact, I think it is fair to say that the whole point of thermodynamics is to sweep vast numbers of the physical degrees of freedom of a system under the rug so that you can treat a system at equilibrium as if it were static even though it really isn't. It is frankly astonishing that this is even possible at all without losing any fidelity in terms of measurable outcomes.) > Some microscopic processes bring the state B to state A, and those break 2nd law. Yes, that's true. The second law is probabilistic. It is "possible" to break the second law in the same sense that it is "possible" for a baseball to quantum-mechanically tunnel through a catcher's mitt. You can do the math to figure the odds in both cases. In fact, actually going through this process is an informative exercise. It isn't difficult. There are some events whose probabilities are so low that the chance of them occurring anywhere in the universe before heat death is barely distinguishable from zero. The odds of actually observing such an event here on earth are vastly smaller still. Both macroscopic tunneling and 2nd law violations are events of this sort. Neither is categorically impossible, but (to put it mildly) it's pretty safe to bet against them nonetheless.
- effie 4y ago
  You have missed my point. The formulation of 2nd law I'm talking about is stating something about all pairs of two MACROstates A,B, not MICROstates, such that B reliably succeeds A after intervention. This pair of MACROstates is not assumed unique, there are hugely many, but formulating the argument uses a single pair. (I'm not a native speaker so don't get distracted by possibly incorrect use of the definite article). The problem with your handwavy argument about macrostates with higher multiplicity is not due to 2nd law being a probabilistic claim. The problem is that it is not clear from that argument alone why it applies to future states, but it does not apply to the past states. To address that, another assumption is needed, such as the asymmetric relation between my macrostates A,B.