entropy empirical? and V8's

[gaara]

hello,

 

i was talkin with a phd student, an he said the 2nd law of thermodynamics, was more of a statistical law, an is based of what has happened. So the 2nd law is empirical in nature. Is that correct in saying? or is entropy, a fact, not just somethign made up to fulfill a consistent observation?

 

also, if anyone knows, why is it uncommon to turbocharge v8's.

[timo]

Afaik, Thermodynamics was originally an empiric branch of physics meaning it was a model trying to describe observations. Modern thermodynamics is based on statistics which indeed makes entropy a statistical variable.

 

Little simplified description of entropy:

If you have a gas in a container you cannot realistically expect to know where each particle is and where it´s heading; a particular state describing the state of each single gas molecule is called a microstate. But you can possibly measure more global properties like the pressure or particle density in different parts of the container; that would be a macrostate.

 

Since you cannot tell in which microstate the system will be, you simply assume that all microstates are equally probable. This is, in fact, just an assumption whose only real justification is that you wouldn´t know of any mechanism that would make one microstate more likely than the other. However, this does not mean that all macrostates are equally probable. Different macrostates can have different numbers of microstates that would lead to them, therefore the relative probability of macrostates is equal to the number of microstates that would lead to them (if each microstate has a probabilily of p, then a macrostate with N microstates leading to it would have the probability N*p).

 

Entropy is simply a measure for the amount of microstates leading to a particular macrostate (it´s proportional to the logarithm of the number of microstates). Tracing this description back, you´ll see how the empiric "systems will most likely be in the state with maximum entropy" becomes a statistical "systems will most likely be in the most likely state" statement.

 

 

I would therefore say that the 2nd law is not empirical in nature, except if you call the assumption of equal probabilities of microstates as empiric (I'd not call it so). It´s not a fact either, given that there´s some assumptions coming in.

 

@V8: Perhaps you should open a seperate thread about that in an appropriate section. Two rather unrelated questions in one thread might lead to confuse overlaps.

[fredrik]

I am not entirely sure about the correct historical thinking, but thermodynamics is one of those parts of physics that can be deduced from application of the ideas of optimal inference. Which means it's minimally speculative, and the "speculations" made are the optimally infered ones, and thus not entirely ad hoc.

 

Entropy is simply a measure for the amount of microstates leading to a particular macrostate (it´s proportional to the logarithm of the number of microstates). Tracing this description back, you´ll see how the empiric "systems will most likely be in the state with maximum entropy" becomes a statistical "systems will most likely be in the most likely state" statement.

 

Another what I think nice generalization statement of the principle of maximum entropy is

 

"macrostates" - can be interpreted as our prior information. Ie. it's everything we know. Can be thought of as patterns and correlations in samples.

 

"microstates" - is interpreted as the apparent degrees of freedom that we see. Can be thought of as samples.

 

Thus a generalized relative entropy can be thought to be a measure of

 

"the degree of uncertainty left, respecting your information at hand"

 

The maxium entropy principles thus becomes a principles of optimal inference. Given our incomptele information, how do we optimally place our bets. It's a bit like game theory. We place our bets as per our updated prior.

 

The point is not that we can expect to be right in any instance, but if we place the bets optimally and respond to the deviations we will learn and evolve (=dynamics). And that's the next step. Deviations updates our priors, also as per some optimal update principle.

 

If we consider our "information at hand" to be static, and never changing, we have an absolute entropy, not relative. But this leads to a problem of the choice of this background prior information? With respect to a gas bottle, we can accept a background prior, but when it comes to elementary and chaotic interactions this breaks down IMO.

 

There is no motivation for a static background prior. It has to evolve to make sense.

 

Since you cannot tell in which microstate the system will be, you simply assume that all microstates are equally probable. This is, in fact, just an assumption whose only real justification is that you wouldn´t know of any mechanism that would make one microstate more likely than the other.

 

I think this can be introduced in a less speculative way. Instead of saying that we "assume", we can consult our prior experience with these microstates(can be thought of as samples). And if they suggest they are equally probable, that is to our knowledge our prior distribution. So it need not be considered as an assumption IMO, it's rather like a best (optimally inferred) guess, unlike an arbitrary guess.

 

Although statistical mechanics is old stuff, it's one of the more beutiful branches of physics, but nevertheless I think we have yet to see the full power of the implications of the underlying principles.

 

/Fredrik

[fredrik]

also, if anyone knows, why is it uncommon to turbocharge v8's.

 

I think you should ask a some vehicle engineer, but from the little I know of cars I think it's basically two philosophies howto increase power.

 

I think that for a given total cylinder volume(displacement) you'd expect to get more peak power with many smaller cylinders as compared to one big one, but I think you get lower torque at lower revs. And the fuel economy I think may suffer.

 

I think this is the idea with turbo, it gives better fuel economy then you don't push the pedal, and also leaves you the power when you need it.

 

So turbo charging a v8 for a standard car (racing is another story) seems like an odd design.

 

Normally the peak power comes at high revs which is not normally reached during normal operation. Therefore I think modern engines are designed instead to give best power and torque during normal revs. Higer revolutions also gives higher noise and poor comfort. If I buy a car I'm more interested in high torque a low rev, and here the turbo I think is better.

 

/Fredrik

[grifter]

well V8 cars are rarely seen as needing turbos, but it is perfectly acceptable to add a turbo to a v8 car, they're mainly bolted on to v4s and v6s to "boost" top speeds and increase mid-range rev' performance. Turbo engines are mainly used for racing (especially drag racing) due to their better performance at top speeds, due to the non-linear power delivery of turbos (turbo-lag); many people choose superchargers for v8's to get more linear power delivery, but to be perfectly honest if your buying a v8 engine (for racing) you've probably got enough money to bi-turbo it therefore significantly increasing power, and top speed.

 

as far as entropy is concerned, Fredrik and Atheists posts covered that perfectly so, no need to repeat what they've said.