Temperature would turn out to be meaningless, simply because a nicely-aimed strike from Maxwell's demon would freeze that boiling kettle and eject one molecule with the many surplus energy. Little doubt the minor eco-friendly Guys have learned this kind of know-how and this accounts with the OMG cosmic rays :)
There's a infamous problem with this structuralist binary reduction: It's not necessarily suitable to identify the Boltzmann and Shannon actions, because the previous is steady (as a result of continual variables like situation) when the latter works more than a finite code-space.
unforgettable thermodynamic portions like enthalpy and Gibbs Electricity to cope with instead of simple and easy Electricity. If any individual is reading this and is questioning exactly what the hell I am speaking about, I "recommend" this Online page: if You're not baffled now you soon will be.
This is when the knowledge-theoretic description of entropy shows its real toughness. In actual fact, the second legislation of thermodynamics is rendered Pretty much trivial by thinking about it from an details-theoretical perspective.
While you correctly report the log W is barely legitimate when every one of the j are Similarly probable. That is real for isolated methods at equilibrium although not otherwise.
I'm continue to wanting to get my head spherical this. It's not fairly as neat and tidy as it may look, as the up coming move would be to presume an Everlasting equilibrium with just the occasional fluctuation in the direction of
When placed on a system that could be in W states, each with equal (**) likelihood p = one/W, it follows that
In fact, if we did know the microstate, just counting attainable states could well be a really lousy measure of entropy - we might be obliged to look at e.g. Kolmogorov complexity rather than basically log W.
I think all of us agree that any state that accidentally shows up in the tossing of ten cash requires ten bits. It would not issue In case the condition is HHHHHHHHHH or TTTTTTTTTT or HHTHTTTHHT. The only thing that matters is the whole quantity of realizations that 'could have been'.
Surely you are doing in any other case how could you say that a box with the many air molecules in one facet has considerably less entropy then 1 with them distribute evenly?
Rene, I believe the extra information and facts that was disregarded from the blog site publish that would assist to reply your concern is usually that what is counted could be the _additional_ info required to specify the microstate provided its macrostate. So in the situation from the N cash, assume that we're now advised the volume of heads.
This analogy can be an clear oversimplification, nonetheless it may have a specific aesthetic usefulness. The idea that info is click here for info conserved by compression to various levels of losslessness (inside fractal dimensions For illustration) and that it
But How about the relation concerning information and facts and entropy? It is straightforward to say "They can be the identical", but deep in my guts I believe it should be a distinction.
Anon -- many thanks on your issue, tends to make me realize I have not been adequately apparent on one significant level.