Timeline for Why is the second law of thermodynamics not symmetric with respect to time reversal?
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| Oct 6, 2021 at 15:52 | comment | added | Harald Rieder | @bolteppa In quantum mechanics entanglement (von Neumann) entropy is also a subjective quantity. It depends on the subjective division of the total Hilbert space into 2 subspaces (and of course on the state vector, too). There is always an infinite number of possible splits, some giving you the max. ("number of qubits") and others the min. 0 and others any number in between. And in a continous space the trace of the density operator mostly will be infinite. To get a finite value invent some subjective coarse grainig.... | |
| Oct 6, 2021 at 10:12 | comment | added | matt_black | The classical notion that all physical laws are symmetric in time depends on the mathematical framework used. Specifically the use of real numbers (with infinite precision). Alternative mathematical number systems (that recognise that infinite precision is not possible in a finite universe) do not give time symmetry in physical laws. So the apparent contradiction may be wrong. | |
| Oct 6, 2021 at 1:18 | comment | added | bolbteppa | @HaraldRieder There's obviously nothing subjective about entropy in statistical mechanics. Your comment about dividing an infinite quantity by something to 'coarse grain' it to make it finite simply makes no sense (classically it's completely unjustifiable to make phase space dimensionless which caused a lot of controversy historically) and is now leading to misunderstandings - given that your comment is being taken seriously, please point out where in section 7 of [1] anything like this is done to set up entropy. | |
| Oct 5, 2021 at 19:26 | comment | added | Harald Rieder | Entropy is a subjective quantity in statistical mechanics. Because it is the expactation value of information you may get out of a part of the world, it should always be infinite. Every continuous variable like x or p encodes an infinite number of bits. To get a finite value you must introduce some coarse graining. This coarse graining comes out of quantum mechanis because [x,p] ~ Planck's constant. | |
| Oct 3, 2021 at 13:30 | history | edited | bolbteppa | CC BY-SA 4.0 |
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| Oct 3, 2021 at 13:23 | history | answered | bolbteppa | CC BY-SA 4.0 |