B What's the fastest the temperature of something can change?

[SpeedOfLightYagami]

Is there a temperature-change equivalent to the speed of light?

 

[Orodruin]

Not really, no.

 

[sophiecentaur]

Is there a temperature-change equivalent to the speed of light?

Perhaps more like the speed of sound.

 

[jbriggs444]

Is there a temperature-change equivalent to the speed of light?

This would be the rate of propagation of a temperature change? In a detonation, that can be quite rapid and can exceed the speed of sound. In a deflagration the propagation is, by definition, lower than the speed of sound.

Or is this the rate at which the temperature at a particular point varies over time? That could be quite rapid in, for instance, a nuclear weapon. Given the thermodynamic definition of temperature, the rate at which an equilibrium can be established would be key. Temperature is technically undefined in the absence of an equilibrium.

 

[DaveE]

Is it fair to speak of the temperature of a single atom? It seems like n=1 is kind of missing the "statistical" part of Statistical Mechanics. 2 atoms?
Anyway, if so it could be as quick as interacting with a photon.

 

[DaveE]

In practice, I'd vote for Ultra Fast Laser Material Processing. Which could be less than a picosecond.

 

[Baluncore]

Is there a temperature-change equivalent to the speed of light?

No.
The rate of temperature rise depends on the energy delivery mechanism.
Stay away from hydrogen bombs.

For a kinetic gas, it is the speed of sound, or the rise-time of the shock front. That increases with the square root of the absolute temperature.

For heating by EM radiation, the front propagates at the speed of light in the dielectric. The particles being heated will accelerate, and depart the scene at a rate, again determined by the rise time of a shock front.

For explosives, it is the energy yield and the molecular weight of the combustion products that decides the propagation of the detonation wave. The time the chemical reaction takes to complete, is the speed of temperature rise.

There are too many scenarios to analyse all. You need to be more specific about the situation.

 

[sophiecentaur]

Is it fair to speak of the temperature of a single atom?

Which one would you choose?

 

[DaveE]

Which one would you choose?

It doesn't make much sense to me for really small systems. Like two atoms one of which was just excited by a photon? 10 atoms? A billion atoms exposed to a terawatt laser pulse? It seems pointlessly pedantic to an engineer like me. But I'm definitely not a physicist. There is much about Temperature, Stat. Mech., Entropy etc. that I don't really understand.

I'll vote for Temperature having no meaning at all without a concurrent description of the application it's being used to describe.

 

[DaveC426913]

There are too many scenarios to analyse all. You need to be more specific about the situation.

He was specific. He only cares about the fastest one.

 

[mfb]

Laser pulses can heat samples from nothing to millions of degrees in a nanosecond.

Heavy ion collisions can change the system from something that doesn't have a well-defined temperature to a trillion degrees in ~10^-23 s.

There is no fundamental limit on temperature rise specifically.

 

[ohwilleke]

TL;DR

Possibly, but not transparently.

Part of the reason that there is no familiar fundamental law bounding temperature changes is that temperature is an emergent description of a system (historically through the statistical mechanical behavior of atoms and molecules although the definition of temperature has been generalized in ways that can apply to other systems). Temperature isn't a truly fundamental physical quantity.

The answer could be that: (1) there is no limit, (2) that the limit is truly immense, or (3) that the question is ill-defined as it approaches the extremes it is asking about.

The question is also ambiguous about whether it is talking about the biggest change that is possible in our actual universe, or about the biggest change that our laws of physics would permit in any arbitrary universe even if it could never happen in our actual universe because the combination of particles in particular states necessary to make that happen are physically impossible to assemble.

Unlike the speed of light, there is certainly no absolute limit on the maximum rates of temperature change in a physically possible system that has practical engineering implications in directly observable physical systems.

But, in any particular well defined class of physical system that is capable of having a well defined temperature and temperature change, you could calculate the rate temperature change that is possible in that particular class of physical systems. See, post #7 for examples.

For example, you could calculate the maximum rate at which the temperature of a system that starts as a drop of water exposed to extremely high frequency photons with a well defined total energy could change.

Long (more advanced than basic) Answer

At the fundamental level there are particles with mass, kinetic energy, spin, frequency, helicity, polarization, etc. But there are ways to define temperature that are very general even in systems where statistical mechanics understandings of thermodynamics are ill-defined.

For example, one can argue there thermodynamic temperature corresponds to momentum or energy transfer in an interaction of two particles, aggregated in some sensible way for a system of more than two particles.

You could argue that there is some maximum level arising from fundamental particle physics laws that ends up putting some sort of bounds on a before and after state in which temperature is defined in a given time period. You would start with the kind of analysis of post #17 in this thread and tweak it to a situation where temperature is defined at each end and consider variation on it where the temperature chance could be greater.

Part of the answer may hinge on the unresolved question of whether there is a UV (i.e. high energy) fixed point in physics at extremely high energies that is absent in the Standard Model of Particle Physics.

Another is the question of the extent to which space-time is continuous or if the continuity of space and time just a very good approximation of reality that in fact breaks space-time into discrete little chunks of a minimum size, with the conventional laws of physics breaking down as you get very close to that minimum size.

For example, it could be that time is discrete and comes in units of Planck time. If so, the minimum elapsed time between states would be one unit of Planck time, and one could conceivably start infinitesimally close to absolute zero and get arbitrarily high in temperature, e.g., with matter-antimatter annihilation in large enough amounts.

Worse yet, in a highly relativistic system involving immense energies on one side of the temperature change, and very small, near Planck scale, distances, the temporal sequence of the events might be observer or coordinate system dependent, and might not even be absolutely causal or local. If a temperature change happens in a space-like rather than time-like interval, you end up with a division by zero problem no matter how big or small the temperature change actually is, which gives you an infinite temperature change per time, which I suppose would amount to proof that there is no such fundamental limit.

Another approach would be to observe that the largest change in temperature per time almost surely happened at the Big Bang, in a way that is physically impossible to recur, and then to try to quantify it. But, while that can get you arbitrarily close to an answer, the singularity at the Big Bang might defy calculation or suggest a limit that approaches infinity as one gets arbitrarily close to the Big Bang singularity of GR.

There is also a lot of theoretical non-consensus about the sequence of events after the Big Bang in the first part of the first second after the Big Bang. The last time I looked, for example, there were at least 118 competing theories of cosmological inflation and there were also alternative theories to the cosmological inflation paradigm. This matters a lot to this question because the brief period of cosmological inflation, if some version of this theory is correct, is probably the moment at which there was the greatest temperature change in the universe of all time, and hence, more or less by definition, the great possible temperature change.

Another definitional issue is the extent to which the Heisenberg uncertainty principle renders any sufficiently small interval of time in a system that can have temperature changes ill-defined. Heisenberg uncertainty concerns would arise well before a classical GR type Big Bang singularity becomes infinite and mathematically intractable.

More generally, conventional wisdom is that in the vicinity of a classical GR singularity like a black hole or the Big Bang, that classical GR is no longer in its domain of applicability and you can only answer these questions with a theory of quantum gravity that does not exist yet, in a full blow, rigorous form.

In conclusion, then, a reliable answer to this question pushes the boundaries of the domain of applicability of "core theory" (i.e. general relativity plus the Standard Model of Particle Physics) in ways that highlight the internal inconsistencies of "core theory" as we understand it today.

 

[DaveC426913]

I gut naively tells me it would limited by the speed of mechanical transmission, but that's not so.

One way something can be heated is by bombarding it with photons, as mfb suggests. And because photons don't abide by Pauli's Exclusion Principle, there is no upper limit on how many can be simultaneously concentrated into a single point.

 

[ohwilleke]

And because photons don't abide by Pauli's Exclusion Principle, there is no upper limit on how many can be simultaneously concentrated into a single point.

Except that, if you get enough mass-energy in a small enough space, it will become a black hole.

Black holes have a well-defined temperature which is a function of their mass, which is almost absolute zero, and closer to zero the more massive they get. So, maybe looking at the transition from a very high temperature pre-black hole state to a black hole near zero temperature transition limit could provide a path to calculating a maximum temperature change rate (or to rigorously proving that no such limit exists, or to placing a lower bound on how high that could be).

There have been papers published about whether it is physically possible for photons alone to form a black hole, but if you have some massive particle pumped up with lots and lots of photons, all bets are off, and it should be possible at least in theory.

 

[Hornbein]

Many clever ideas here. I'll note that it is expected that in the superfluid cores of neutron stars the propagation of temperature changes is about half the speed of light.