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Entropy isn't a function of imperfect knowledge. It's a function of the possible states of a system and their probability distributions. Quantum mechanics assum
by logicchains 1y ago
Entropy isn't a function of imperfect knowledge. It's a function of the possible states of a system and their probability distributions. Quantum mechanics assumes, as the name implies, that reality at the smallest level can be quantised, so it's completely appropriate to apply entropy to describing things at the microscopic scale.
- kgwgk 1y ago> Entropy isn't a function of imperfect knowledge. It's a function of the possible states of a system and their probability distributions. There are no probability distributions over possible states when there is perfect knowledge of the state. > Quantum mechanics Entropy is also zero for a pure quantum state. You won’t have entropy without imperfect knowledge.
- whereismyacc 1y ago> There are no probability distributions over possible states when there is perfect knowledge of the state. I know very little about physics but I thought that the leading interpretations of quantum physics say that the probability distribution is all we can know about a system. The entropy is not due to due to a lack of information about the quantum state, but because the outcomes are inherently stochastic?
- kgwgk 1y agoEntropy is about the state - not about “outcomes”. “All we can know” is the precise state - at least in principle - and entropy is zero in that case.
- mr_mitm 1y agoJust look at the definition of entropy. Knowledge about a system never enters the equation. S := -k_B sum p_i ln (p_i)
- kgwgk 1y agop_i Edit to add lots of words: In the definition of entropy S := -k_B sum p_i ln (p_i) knowledge about the system enters the equation in the p_i terms. The other term is a constant so it’s not like there are many other choices to link the entropy to the system!
- mr_mitm 1y agoPlease communicate in full sentences with me. I can only guess that your objection is something about probabilities. A microstate has a probability independent of my knowledge of the system just like the probability of having a royal flush doesn't change after drawing five cards. The probability of me ending the game with a royal flush might, but that is not what we mean by these probabilities.
- kgwgk 1y agoThe same microstate will have different probabilities depending on what are the constraints or measurements used in _your_ description of the system. If you choose to describe the system using its microstate - and you know it - there are no probabilities anywhere. You can of course know something and choose to ignore it - the entropy is still a reflection of the uncertainty (actual or for the sake of a lower-resolution model).
- tsimionescu 1y agoBut the point is that, regardless of how you choose to describe or even measure the system, it will need exactly as much heat to raise its temperature by 1 degree (or it will need as much kinetic energy to increase the average velocity of the constituents by the same amount, in the microstate framework). So there is some objective nature to entropy, it's not merely a function of subjective knowledge of a system. Or, to put it another way, two observers with different amounts of information on the microstate of a system will still measure it as having the same entropy.
- 1y ago
- aurareturn 1y agoIf we knew the exact state of all particles in an enclosed system, we can calculate what future states will be exactly. No need to calculate possible states.
- IAmBroom 1y agoSince that's not possible in any physical system of one or more particles, it's irrelevant.
- mensetmanusman 1y agoQuantum uncertainty actually says no to this. There is an ‘error’ in any propagating probability field.