Can pressure be negative?

[Ziggurat]

If it starts cavitating once the absolute pressure becomes just zero, much less negative, how can it "go" to "significant negative absolute pressure"?

In something like sea water, cavitation can be nucleated at fairly low negative pressures because of impurities, dissolved gasses, and turbulence (which can create local fluctuations to larger negative pressures). But note that you still need to go to actual negative pressures, not just zero pressure. That's why the negative relative pressure needs to be larger than the ambient pressure. That's why the water vapor pressure is included: that's the negative pressure you need to reach in order for nucleated bubbles to start expanding.

If you use very pure water, without dissolved gasses, then you can avoid nucleation until very large negative pressures.

 

[W.D.Clinger]

Relative to what reference, he queried.

Any inertial frame in Newtonian mechanics or special relativity. If the object is stationary with respect to some inertial frame, then its acceleration will be zero with respect to any other inertial frame.

If you'd prefer an example drawn from general relativity, consider

R_μν-½Rg_μν+Λg_μν=8πT_μν (in natural units)​

Via a mathematical transformation that might be recognized even by engineers, that's equivalent to

0=R_μν-½Rg_μν+Λg_μν-8πT_μν​

Here 0 is a tensor, so it's independent of reference frames. (To state that more correctly, it's independent of coordinate systems.)

Any law of physics that's stated as an equality can be stated as an equality between 0 and the difference of the two sides. In that form, the law becomes an invariant of nature: a certain calculation always yields zero.

That's not quite the same as saying zero exists in nature. As several people have stated, the concept of number is used in science to describe nature, with no ontological commitment to the existence of numbers themselves in nature (apart from the fact that we think our thoughts are part of the real world, and we think we think about numbers). That's a terribly pedantic point. By and large, the people who have been making that pedantic point in this thread don't appear to understand that it applies equally to all numbers, not just to zero or to negative numbers.

Your arguments are, to an engineer, all semantics. So we're even.

I have worked with engineers for several decades, so I'm well aware of their tendency to insist rather stubbornly upon giving priority to the limited and/or simplified definitions they were taught as undergraduates. Having taught courses designed for engineers, I also understand the pedagogical value of feeding them limited and/or simplified definitions.

The preceding paragraph should be generalized beyond engineers. Everyone is taught limited and/or simplified definitions of scientific and mathematical concepts, and everyone tends to hold onto the version they've been taught (or, in many cases, the moderately botched version that made its way into their heads). Need I mention that some people are more stubborn than others?

I gave an example of that tendency on the very first page of this thread. That example also showed how Wikipedia's treatment of some scientific and mathematical concepts has been distorted by the preponderance of engineers over scientists and mathematicians.

 

[Ziggurat]

Actually I would think that if T can diverge under some real conditions in our model but not in reality, I would reconsider my model and my definition of T.

And why do you think that temperature diverges in the model but NOT in reality? This isn't a case where the model predicts something that experiments contradict. The model predicts the experiments quite accurately. Why is it a problem to have an infinite temperature?

Perhaps this β is a very useful concept but not fundamental if it allows for an infinite T, which is supposed to represent the kinetic energy of an object.

But that's just it: that's NOT what temperature represents. It never actually did, and with good reason. If you define it that way, you'll find that thermal equilibrium can occur between systems in thermal contact which have different temperatures. Such a definition rather defeats the purpose of defining a temperature, doesn't it?

That common perception of temperature comes in large part from the equipartition theorem. That's a result of thermodynamics and the standard definition of temperature, but it does not apply to all systems (in fact, any system with a varying heat capacity violates equipartition), and it always breaks down at very low temperature. Negative temperature systems are just an extreme example of the breakdown of the equipartition theorem, but they're hardly the only example.

In effect, defining temperature in terms of the equipartition theorem is a convenient lie. It's simple, and it's accurate enough for enough of the time that it gets taught as if it defined temperature, because the truth too complex for beginning students. You can't teach the real definition of temperature without entropy and calculus, and it's still useful to have an operational (if wrong) working definition even if you aren't ready for the real thing.

 

[rwguinn]

Any inertial frame in Newtonian mechanics or special relativity. If the object is stationary with respect to some inertial frame, then its acceleration will be zero with respect to any other inertial frame.

If you'd prefer an example drawn from general relativity, consider

R_μν-½Rg_μν+Λg_μν=8πT_μν (in natural units)​

Via a mathematical transformation that might be recognized even by engineers, that's equivalent to

0=R_μν-½Rg_μν+Λg_μν-8πT_μν​

Here 0 is a tensor, so it's independent of reference frames. (To state that more correctly, it's independent of coordinate systems.)

Any law of physics that's stated as an equality can be stated as an equality between 0 and the difference of the two sides. In that form, the law becomes an invariant of nature: a certain calculation always yields zero.

That's not quite the same as saying zero exists in nature. As several people have stated, the concept of number is used in science to describe nature, with no ontological commitment to the existence of numbers themselves in nature (apart from the fact that we think our thoughts are part of the real world, and we think we think about numbers). That's a terribly pedantic point. By and large, the people who have been making that pedantic point in this thread don't appear to understand that it applies equally to all numbers, not just to zero or to negative numbers.


I have worked with engineers for several decades, so I'm well aware of their tendency to insist rather stubbornly upon giving priority to the limited and/or simplified definitions they were taught as undergraduates. Having taught courses designed for engineers, I also understand the pedagogical value of feeding them limited and/or simplified definitions.

The preceding paragraph should be generalized beyond engineers. Everyone is taught limited and/or simplified definitions of scientific and mathematical concepts, and everyone tends to hold onto the version they've been taught (or, in many cases, the moderately botched version that made its way into their heads). Need I mention that some people are more stubborn than others?

I gave an example of that tendency on the very first page of this thread. That example also showed how Wikipedia's treatment of some scientific and mathematical concepts has been distorted by the preponderance of engineers over scientists and mathematicians.

All of the above.
I am, indeed, well aware of the concept of Zero, and could not do my work without it.
but zero is a concept, defined by the system in which one works. I was simply pointing out that ziggy's hydro/cavitation problem doe not yield absolute pressures < 0, simply because of water's property to become vapor and solid at zero pressure absolute. If you put water is a cylinder, and add a piston that perfectly seals to the bore, and start pulling on it, part of the water will turn to a vapor and keep expanding as P->0 psia, so it's a poor example of "negative pressure".
I will concede that negative pressure might exist at a quantum level. I'm not willing to do so at a macro level

 

[Ziggurat]

All of the above.
I am, indeed, well aware of the concept of Zero, and could not do my work without it.
but zero is a concept, defined by the system in which one works. I was simply pointing out that ziggy's hydro/cavitation problem doe not yield absolute pressures < 0, simply because of water's property to become vapor and solid at zero pressure absolute. If you put water is a cylinder, and add a piston that perfectly seals to the bore, and start pulling on it, part of the water will turn to a vapor and keep expanding as P->0 psia, so it's a poor example of "negative pressure".

No, rwguinn. Negative absolute pressures DO occur in such experiments. Your intuition misguides you. While equilibrium would involve the creation of vapor and/or solid states, metastable negative pressures can be and are obtained experimentally.

I will concede that negative pressure might exist at a quantum level. I'm not willing to do so at a macro level

That's a shame. Because there's a lot of literature on the subject. For example:
http://jcp.aip.org/resource/1/jcpsa6/v133/i17/p174507_s1
And here's a more general article on the topic:
http://www.aip.org/pt/feb00/maris.htm
The second link is a better read, but the first is an example of the continued interest in the topic in peer-reviewed literature (not the existence off negative pressure, which is well settled, but what the exact phase diagram looks like in that regime).

I really don't understand why you're having a hard time accepting negative pressures. Metastability is well established theoretically, negative absolute pressures have been observed in water and other liquids with many different experimental techniques, and it has direct engineering-relevant consequences. So what's the problem?

 

[Perpetual Student]

Ziggurat

Perhaps this β is a very useful concept but not fundamental if it allows for an infinite T, which is supposed to represent the kinetic energy of an object.

But that's just it: that's NOT what temperature represents. It never actually did, and with good reason. If you define it that way, you'll find that thermal equilibrium can occur between systems in thermal contact which have different temperatures. Such a definition rather defeats the purpose of defining a temperature, doesn't it?

So, that is the problem. My intuitive notion of T (representing -- or proportional to -- the average molecular kinetic energy of an object) differs significantly from the definition of T in statistical mechanics. I had erroneously assumed they were very similar but differed only in the quantum realm. My familiar definition of T is not useful in physics because of the difficulties you mention. Would it not be reasonable to say that this T is not the same entity as my familiar T, which cannot be infinite since the average kinetic energy of an object cannot be infinite? When one says "temperature" the esoteric definition you are referring to is not what comes to mind when I say it cannot be infinite.
So, in summary, I assume we can agree that:
1. There is such a thing as the average kinetic energy of an object and,
2. It cannot be infinite.
Is that true?

 

[rwguinn]

No, rwguinn. Negative absolute pressures DO occur in such experiments. Your intuition misguides you. While equilibrium would involve the creation of vapor and/or solid states, metastable negative pressures can be and are obtained experimentally.



That's a shame. Because there's a lot of literature on the subject. For example:
http://jcp.aip.org/resource/1/jcpsa6/v133/i17/p174507_s1
And here's a more general article on the topic:
http://www.aip.org/pt/feb00/maris.htm
The second link is a better read, but the first is an example of the continued interest in the topic in peer-reviewed literature (not the existence off negative pressure, which is well settled, but what the exact phase diagram looks like in that regime).

I really don't understand why you're having a hard time accepting negative pressures. Metastability is well established theoretically, negative absolute pressures have been observed in water and other liquids with many different experimental techniques, and it has direct engineering-relevant consequences. So what's the problem?

No problem. But i'd like the goalpost to remain fixed at some point.
Yes, I use negative pressure-all the time. Sometimes I call it tension. It all depends on where I set my zero.

 

[W.D.Clinger]

First, a correction:

Any inertial frame in Newtonian mechanics or special relativity.

The highlighted part is wrong. I shouldn't have tried to use a single sentence to describe the admissible reference frames for both Newtonian mechanics and special relativity. If you caught my mistake, you probably know how to repair it.

I will concede that negative pressure might exist at a quantum level. I'm not willing to do so at a macro level

I hear ya, and I appreciate the civility of your discussion.

As for the macro level, however, I'd point out that Tim Thompson's discussion of how a positive cosmological constant creates negative pressure is significant only at cosmological scales, which are about as macro as you can get. To quote another paragraph from Weinberg's Cosmology, page 9:

• Vacuum energy: As we will see in Section 1.5, there is another kind of energy-momentum tensor, for which T^μν ∝ g^μν, so that p = -ρ, in which case the solution of Eq. (1.1.32) is that ρ is a constant, known (up to conventional numerical factors) either as the cosmological constant or the vacuum energy.

Weinberg's talking about the de Sitter solution in which the Λg_μν term of Einstein's field equations, which I used as an example in my previous post, dominates the curvature terms. From equation (1.1.32) on page 8, it's obvious that p = -ρ implies ρ is constant. From p = -ρ, it's obvious that a positive vacuum energy proportional to ρ corresponds to negative pressure p.

 

[Ziggurat]

So, that is the problem. My intuitive notion of T (representing -- or proportional to -- the average molecular kinetic energy of an object) differs significantly from the definition of T in statistical mechanics. I had erroneously assumed they were very similar but differed only in the quantum realm. My familiar definition of T is not useful in physics because of the difficulties you mention.

Yes.

Would it not be reasonable to say that this T is not the same entity as my familiar T, which cannot be infinite since the average kinetic energy of an object cannot be infinite? When one says "temperature" the esoteric definition you are referring to is not what comes to mind when I say it cannot be infinite.

Sure. I'd call it the "rigorous" or "technical" definition of temperature, not the "esoteric" one, but that's a semantic preference on my part, I can accept other people having other preferences.

So, in summary, I assume we can agree that:
1. There is such a thing as the average kinetic energy of an object and,
2. It cannot be infinite.
Is that true?

Yes, that is indeed quite true.

 

[Perpetual Student]

Yes.



Sure. I'd call it the "rigorous" or "technical" definition of temperature, not the "esoteric" one, but that's a semantic preference on my part, I can accept other people having other preferences.



Yes, that is indeed quite true.

Thanks for your responses. I am curious, why does "average kinetic energy" not have some convenient unit of measure or notation like Ξ = (1/2)mv_rms² ?
Assuming not, why not, since it seems to be an important concept.

 

[Ziggurat]

Thanks for your responses. I am curious, why does "average kinetic energy" not have some convenient unit of measure or notation like Ξ = (1/2)mv_rms² ?
Assuming not, why not, since it seems to be an important concept.

Two things come to mind. First, the term would have some limitations. In an ideal gas, the thermal energy is almost purely kinetic. But in solids, only half of the thermal energy is kinetic energy, the other half is increased potential energy. That's why the molar specific heat of a monatomic ideal gas is 3R/2, but the molar specific heat of solids (at sufficiently high temperatures) is 3R. If what you care about is the thermal energy (which can be both kinetic and potential), then measuring kinetic energy isn't what you want anyways.

Second, in cases where you want to know kinetic energy specifically, the equipartition theorem usually does apply. So temperature already tells you what you want to know for such cases. It seems a bit unnecessary to invent a new term to handle the few cases where equipartition doesn't apply AND you need the kinetic energy, not the total thermal energy. One certainly could do so, but without a lot of use for a specific term, it's not likely to catch on.

 

[Perpetual Student]

Well, I made a only a fleeting effort, but in spite of a fairly good background in mathematics, trying to understand the modern definition of T given by statistical mechanics is a tough project for a layman. It is bizarre that Mozina could actually believe he can have any position from which to make judgements about such a subject without a strong knowledge of physics and mathematics. As many of us surely recognize, it is also quite pathetic!

 

[Ziggurat]

Well, I made a only a fleeting effort, but in spite of a fairly good background in mathematics, trying to understand the modern definition of T given by statistical mechanics is a tough project for a layman.

Yes, it is. Once you get over the hurdle, it becomes quite clear why temperature is defined in this manner, but the hurdle isn't low. Most people (even in the non-physics sciences) never need to learn it. I've never faulted anyone for not knowing this stuff.

It is bizarre that Mozina could actually believe he can have any position from which to make judgements about such a subject without a strong knowledge of physics and mathematics. As many of us surely recognize, it is also quite pathetic!

There isn't really any rational explanation for his behavior in this regard.

 

[Calrid]

Oh and one more thing the only thing infinities do in experiments is provide limits to systems, where things (by which I mean anything material or energetic or non conceptual) that are actually infinite are impossible.

The renormalisation of the probability distribution of a wave function is a good example, because waves have only certain freedoms we can discount (or at least make statistically insignificant) the chance of the wave moving instantly to point [latex] x_1[/latex] from point [latex]x_0[/latex] where we assume each point is discrete and physically distant. So the limits of the integral become:

[latex]\int_{-\infty}^{\infty}x\;\; dx[/latex]

Where x is any system we wish to model, in this case it could involve the Dirac or Schrodinger equation or more basically just the energy/h bar.

When we square the wave function negatives disappear so we end up with:

[latex]\int_{0}^{\infty}x\;\; dx[/latex]

Note both 0 and infinity are asymptotes in our system. Energy cannot be infinite or 0.

This isn't really a problem as already stated energy or probabilities can not be negative anyway, something either is somewhere or it is not somewhere it cannot have a negative probability of being somewhere any more than it can have negative energy.

So anyway basically in a Minkowski metric because infinite energy is impossible, a ship travelling can approach c, but because of time-space dilation, it cannot actually reach it. It's rather like division by infinity or perhaps more appropriately manipulation of something beyond any numerical bound, or to put it another way because of time dilation it takes infinite time to reach c as speed approaches c at the asymptote limit of c. It should theoretically be possible only for a mass object to reach c, at least in the equations, only if its acceleration is instantaneous and its speed hence is c instantaneously, although that is a rather hypothetical assertion. So we just say that no object that has mass can achieve c.

Science dislikes infinities it is for this reason quantum mechanics breaks down at the singularity and new metrics are needed to model the gravitational concerns so that infinities do not make the equations nonsensical.

Infinity in experiment is a limit. If your energy concerns are infinite, then they contain more energy than there is in the whole universe and you just ********** up. If they are a limit to which energy concerns can approach asymptotically then you just renormalised something so that it is within statistical limits that can be modelled by actual experiment.

Anyone who says that the energy of an actual particle, say a phonon, is infinite at (x,t) is either a crackpot or insane or a moron.

There's a good reason also why the anti particle of a photon is itself but that's beside the point.

 

[sol invictus]

. I just said 0 and infinity are concepts, they cannot and will never exist in a physical universe.
...
If you want to keep arguing your straw man go for it but I never said anything about negatives I only opined on 0 and infinity. Get over it.

I never at any point claimed negatives didn't exist hell quantum mechanics is based on them or at least the squaring of imaginary or real numbers is in a wave function equation. What are you arguing about. I just said 0 and infinity are concepts, they cannot and will never exist in a physical universe.

I'm sorry Calrid, but your position is incomprehensible. If your argument was that numbers don't exist because they're an abstraction, it would at least be coherent. But instead, your argument seems to be that negative numbers exist, positive numbers exist, even complex numbers exist - but zero doesn't.

To be blunt, that's simply nonsense. Zero is just another number, and the whole construction of real (and complex) numbers makes no sense without it. The same goes for infinity, as the example of negative temperature illustrates quite nicely.

 

[DeiRenDopa]

I just said 0 and infinity are concepts, they cannot and will never exist in a physical universe.

In the US, there is a temperature scale in wide use, called Fahrenheit; in most of the rest of the world the comparable scale is called Celsius.

In many places where the Celsius scale is used, on many days every year, the daily maximum temperature - as measured at a weather station - is given as some number >0, and the minimum as some number <0.

At some time during such days, was the temperature 0 (degrees) C?

In some places in the US, on quite a few days every year, the daily maximum temperature - as measured at a weather station - is given as some number >0, and the minimum as some number <0.

At some time during such days, was the temperature 0 (degrees) F?

Suppose I invent a new temperature scale, which I define as being related to the Celsius scale as follows:

degrees DRD = ln (degrees C)

On one of those max>0C & min<0C days, does the temperature - as measured using the DRD scale - ever become infinite (positive or negative)?

 

[rwguinn]

All of this discussion reminds me of something one of my prefessors said once--paraphrasing:
If your results are negative numbers, then you have probably set zero at too high a value.

 

[W.D.Clinger]

infinities and limits

Two sayings attributed to Albert Einstein:

• Only two things are infinite, the universe and human stupidity, and I'm not sure about the former.
• The difference between stupidity and genius is that genius has its limits.

Oh and one more thing the only thing infinities do in experiments is provide limits to systems, where things (by which I mean anything material or energetic or non conceptual) that are actually infinite are impossible.

The renormalisation of the probability distribution of a wave function is a good example, because waves have only certain freedoms we can discount (or at least make statistically insignificant) the chance of the wave moving instantly to point [latex] x_1[/latex] from point [latex]x_0[/latex] where we assume each point is discrete and physically distant. So the limits of the integral become:

[latex]\int_{-\infty}^{\infty}x\;\; dx[/latex]

Where x is any system we wish to model, in this case it could involve the Dirac or Schrodinger equation or more basically just the energy/h bar.

When we square the wave function negatives disappear so we end up with:

[latex]\int_{0}^{\infty}x\;\; dx[/latex]

Note both 0 and infinity are asymptotes in our system. Energy cannot be infinite or 0.

The passage quoted above suggests that its author would benefit from a review of freshman calculus:

• The upper and lower limits of integration are not limits in the same sense that the value of the integral is the limit of a infinite sequence of increasingly accurate approximations.
• Squaring the magnitude of a wave function (or multiplying it by its complex conjugate) is not remotely equivalent to changing the lower limit of integration from negative infinity to zero.
• There is no reason to assume that either zero or infinity will be an asymptote of "any system we wish to model."

It's hard to hide such basic misconceptions by burying them under an avalanche of phrases such as "renormalization", "the probability distribution of a wave function", "statistically insignificant", "assume each point is discrete", "Dirac or Schrodinger equation", or "energy/h bar".

 

[Ziggurat]

The renormalisation of the probability distribution of a wave function is a good example, because waves have only certain freedoms we can discount (or at least make statistically insignificant) the chance of the wave moving instantly to point [latex] x_1[/latex] from point [latex]x_0[/latex] where we assume each point is discrete and physically distant. So the limits of the integral become:

[latex]\int_{-\infty}^{\infty}x\;\; dx[/latex]

Where x is any system we wish to model, in this case it could involve the Dirac or Schrodinger equation or more basically just the energy/h bar.

Presumably you mean
[latex]\int_{-\infty}^{\infty}f(x)\;\; dx[/latex]
because what you wrote is a specific integral, with a specific solution (ie, zero).

When we square the wave function negatives disappear so we end up with:

[latex]\int_{0}^{\infty}x\;\; dx[/latex]

Uh, no. That's NOT what we get. Squaring the wave function squares what's inside the integral (which isn't x), it does nothing to the limits of integration.

Note both 0 and infinity are asymptotes in our system.

No, they are limits of integration. Not the same thing at all.

Energy cannot be infinite or 0.

Energy cannot be infinite within a finite region of space under any sensible definition. It can be zero, depending on your definition. But nothing you wrote above has anything to do with energy.

So anyway basically in a Minkowski metric because infinite energy is impossible, a ship travelling can approach c, but because of time-space dilation, it cannot actually reach it. It's rather like division by infinity or perhaps more appropriately manipulation of something beyond any numerical bound

Division by infinity is quite well-behaved. There are no problems with it. A velocity of c produces a division by zero, not infinity, and division by zero is the problematic one.

Science dislikes infinities

Science has no feelings. YOU dislike infinities.

Infinity in experiment is a limit. If your energy concerns are infinite

You don't need infinite energy to reach infinite temperatures, given the right system (namely, any system which has a maximum possible energy).

Anyone who says that the energy of an actual particle, say a phonon, is infinite at (x,t) is either a crackpot or insane or a moron.

Good thing, then, that nobody here made any such claim.

 

[Tim Thompson]

Thermodynamic Temperature

... trying to understand the modern definition of T given by statistical mechanics is a tough project for a layman.

I think you will find that our "intuitive" definition of temperature as related to the average kinetic energy of particles is in fact the more modern version. After all, one cannot even consider the idea of particle kinetic energy until one has particles to consider, and before the rise of atoms & molecules in modern physics, this was not the case. The idea dates from the kinetic theory of gases (Boltzmann, Maxwell, & etc.), but the positive existence of molecules (and by inference atoms as well) was not finally nailed down until Einstein did it in 1905 with the publication of his PhD thesis, A New Determination of Molecular Dimensions. Indeed, look at Ziggurat's inverse temperature (Beta = 1/k_BT) and look at the Wiki page for the Boltzmann Distribution and you can see that this inverse temperature comes directly from the idea of temperature as the average kinetic energy of the particles. It's just a different formulation of the same idea.

On the other hand, the idea of temperature as a "state variable", without any consideration of particle kinetic energy, is rather older than that. While Maxwell is famous for his "Maxwell's Equations" of electromagnetism, he is also the founder of the less well known Maxwell's Equations of Thermodynamics, which are just as fundamental and basic in their own discipline as their more famous siblings. So when we look at a standard textbook, like Fundamentals of Classical and Statistical Thermodynamics (Bimalendu Roy, John Wiley & Sons, 2002), we find his definition of "thermodynamic temperature" on page 159, equation 7.39:

[latex]\dfrac{1}{T} = (\frac {\partial S}{\partial U})_V[/latex]

Here T is the temperature, S is entropy, U is the internal energy, while the subscript v indicates a process at constant volume. Quoting Roy: "Although we have restricted our definition of thermodynamic temperature to simple compressible substances, this definition may be extended to other classes of substance." Indeed, we can see that Roy's definition comes straight out of Maxwell's thermodynamic equations ... dU = TdS - pdV where pdV goes away if the volume is constant.

But Maxwell's equations of thermodynamics are all derived from classical thermodynamics, where everything including temperature is simply a state variable, with no reference to any particles or their kinetic energies. The great accomplishment of the founders of statistical mechanics is that they were able to find statistical equivalents for the non-statistical properties of classical thermodynamics, preserving all of known physics in the process. That's a pretty cool job to pull off.

So this is not a "modern" definition of T unless one chooses to stretch the idea of "modern". All of the ideas were established in the 19th century, even if they did not all become common place until the early 20th century. But it's a cinch that the idea of thermodynamic temperature from Ziggurat's posts is well over 100 years old.

As long as one is restricted to the worm's eye view of temperature slavishly tied to particle kinetic energy, then one cannot understand or accept the idea of negative temperature. But then that is just the hollow voice of ignorance in any case. Once we understand the more general physical definitions then negative thermodynamic temperatures are no more amazing than negative non-thermodynamic temperatures, simply negative values for state variables of a system, as if that were some kind of big deal.

For pressure, it's even easier. While temperature is usually, but not always, a scalar quantity, pressure is properly a vector quantity in classical physics, because it is a force per unit area (and even areas can be vectorized as a unit length vector orthogonal to the surface). So pressure this-a-way is positive, while pressure that-a-way is negative. It's all about how you define what "positive" and "negative" mean, and I haven't seen any efforts along those lines yet.

And of course, need I say, this was supposed to be a discussion of pressure not temperature, though we seem to have left the straight and narrow path once again to tread in dangerous waters.