51–60 of 295 posts
Earlier quoted context omitted.
OP is about as good as any explanation I've seen.
"Compressibility" (in the software sense) would perhaps carry the most meaning. Entropy is ultimately all about the ability to extract information (i.e. work) out of a system.
The author mentions Boltzman brains and that a human body could theoretically spontaneously form out of particles given a long enough time span. Of course, nothing like this can ever happen. It’s the fallacy of thinking infinite time means infinite possibilities.
This podcast episode has a good discussion on the subject: https://universetoday.fireside.fm/745
One aspect of entropy that I always find counterintuitive is that unlike mass, charge, etc. it is not a physical quantity. In fact, from the point of view of an experimenter with perfect information about a physical system, the entropy of the system is exactly conserved over time (as made precise by Liouville's Theorem). The Second Law survives in this setting only in the most trivial sense that a constant function d…
Not really. Even from a point of view of an experimenter with perfect information, the entropy of the system declines over time as fewer and fewer bits are needed to describe the system. For example, start with a Glas of warm water and an ice cube in it. Over time, the ice will melt and the range of different temperatures of the molecules decline. Consequently, you need fewer and fewer bits to describe the complete s…
Furthermore, velocity is also a product of direction as much as speed, so if you take into consideration a solid object may vibrate it's particles in the same direction while a liquid can have it's particles in infinite directions, you're talking about way more information you have to encode.
One aspect of entropy that I always find counterintuitive is that unlike mass, charge, etc. it is not a physical quantity. In fact, from the point of view of an experimenter with perfect information about a physical system, the entropy of the system is exactly conserved over time (as made precise by Liouville's Theorem). The Second Law survives in this setting only in the most trivial sense that a constant function d…
The article describes it as a measure of hidden information in a system, which is a good description. But that's not a property of the system itself, it's a property of the observer, from whom the information is hidden.
So different observers with different information about a system will have different opinions about its entropy.
My password, for example, to me has zero entropy. I know its microstate. But it's quite secure from someone trying to guess it, and they will think it's quite high in entropy.
If all you know about a system is that it's a kilogram of air at room temperature, it will seem quite high in entropy to you, as many possible microstates are consistent with that description. But if you have godlike knowledge of the exact configuration of every particle in the container, it will seem very low in entropy to you, and that's more than just an accounting difference. Indeed you can use that information to operate a Maxwell's demon and turn the system into a heat engine, splitting the cold and hot molecules into separate spaces and extracting work as though the system really had low entropy to start with. Because it did. To you.
Most of the confusion about entropy comes from what Jaynes calls the mind projection fallacy: the tendency to treat our uncertainty about a system as a property of the system, rather than a property of ourselves.
The author mentions Boltzman brains and that a human body could theoretically spontaneously form out of particles given a long enough time span. Of course, nothing like this can ever happen. It’s the fallacy of thinking infinite time means infinite possibilities.
One aspect of entropy that I always find counterintuitive is that unlike mass, charge, etc. it is not a physical quantity. In fact, from the point of view of an experimenter with perfect information about a physical system, the entropy of the system is exactly conserved over time (as made precise by Liouville's Theorem). The Second Law survives in this setting only in the most trivial sense that a constant function d…
To be honest, I hadn't heard of Louisville's Theorem before but it doesn't seem to imply what you're saying -- in fact it is used to prove the fluctuation theorem which quantifies the probability of entropy spontaneously decreasing (as thermodynamic entropy is a statistical effect).
Earlier quoted context omitted.
> that a human body could theoretically spontaneously form out of particles given a long enough time span. To be fair, isn't this precisely what happened?
If you leave out "spontaneously"!
"Spontaneous" can be defined a few different ways: https://www.merriam-webster.com/dictionary/spontaneous
From the link "2: arising from a momentary impulse" you get the implied meaning from the original comment if you assume standard human experience of a "moment" IE a few seconds or less.
However you could argue that human evolution is but a moment in the scope of the universe.
And then with definition "5: developing or occurring without apparent external influence, force, cause, or treatment"
The only way it wouldn't be spontaneous would be if an external actor (Deity of your choice?) directed human evolution somehow. To say this is debatable is an understatement..
And so we have fun in word play and hopefully appreciation of different viewpoints.
:-)
edit: rearranged for better flow
One aspect of entropy that I always find counterintuitive is that unlike mass, charge, etc. it is not a physical quantity. In fact, from the point of view of an experimenter with perfect information about a physical system, the entropy of the system is exactly conserved over time (as made precise by Liouville's Theorem). The Second Law survives in this setting only in the most trivial sense that a constant function d…
If I can pick your brain, there’s a related concept — entropy production. How does that relate with these ideas?
To produce entropy you have to grow the number of possible microstates that are consistent with available knowledge of the macrostate.
Usually you accomplish that by converting stored energy into heat somehow. A charged capacitor has low entropy compared for the energy it holds; discharge it through a resistor, and you produce a bunch of entropy because that energy can now be distributed in a lot more ways among a lot more degrees of freedom, and nobody can possibly keep track of them.
I thought the 2nd law of thermodynamics was saying that with incomplete knowledge, the probability distribution of possible states becomes more and more spread out as time goes on. It's almost a limit to how you can make predictions or simulations of physics when the initial state of the system is not fully known. Equivalently, it's a banal statement about chaos in the sense of chaos theory.
The only thing I don't get is how physicists get around the discrete and finite restriction. Maybe the state of the system is not what has entropy. Rather, one can define an arbitrary function f from the system to a finite set S, and then talk about the entropy of f(System at time t), because this is indeed a discrete and finite probability distribution which you can take the entropy of.
Hmmm. Maybe I understand entropy.
The author mentions Boltzman brains and that a human body could theoretically spontaneously form out of particles given a long enough time span. Of course, nothing like this can ever happen. It’s the fallacy of thinking infinite time means infinite possibilities.
> that a human body could theoretically spontaneously form out of particles given a long enough time span. To be fair, isn't this precisely what happened?