B Can Relativistic Effects Alter Thermodynamic Processes in Experiments?

[bwana]

TL;DR Summary

is there evidence of relativistic change in processes occurring at the level of large populations of particles

In most experiments of SR, we look at atomic and subatomic particles or the frequency of EM radiation.

The Haefele-Keating experiment looked at the resonance of cesium atoms stimulated by a certain EM frequency
https://en.wikipedia.org/wiki/Hafele–Keating_experiment

The Ives-Stillwell experiment looked at Doppler shift
https://en.wikipedia.org/wiki/Ives–Stilwell_experiment

The lifetimes of muons and other particles were investigated in other experiments.
https://en.wikipedia.org/wiki/Experimental_testing_of_time_dilation

But consider the mundane process of diffusion. Does diffusion occur more slowly in a container moving close to relativistic velocity? I guess doing this experiment is technically very difficult. But haven't we developed tools improved enough to allow this?

Or consider the Carnot cycle. Or perhaps something even more fundamental- heat transfer between two bodies. A simple experiment would consist of an insulated (adiabatic) container. In this container are two separate containers of water separated by a gap of air. Each container has a thermocouple to measure its temperature. One container is then heated to a specific temperature. The containers are brought into contact and the time it takes for the temperature equilibration is measured and a curve is generated. If this experiment is done on an airplane (like the Hafele–Keating_experiment) we should expect different rates of cooling compared to the ground experiment as well as the direction of flight compared to the ground (as in the Hafele–Keating_experiment)

But the theory of relativistic thermodynamics is still controversial
https://www.nature.com/articles/s41598-017-17526-4
The initial treatment by Planck and Einstein suggested

\begin{array}{ccc}T^{\prime} =\frac{T}{\gamma }\,, & S^{\prime} =S, & p^{\prime} =p\,,\end{array}where γ = (1 − (w/c))−1/2 is the Lorentz factor, c is the speed of light, and primed quantities correspond to the thermodynamic measurements in I’. These results mean that a body should appear cooler for a moving observer, but both entropy and pressure are relativistic invariants.

But even to this day, there is no consensus about how to theoretically treat relativistic thermodynamics. Even when the theory is written down, I can make no sense of it.
https://arxiv.org/abs/gr-qc/9803007
https://link.springer.com/article/10.1007/s10701-020-00393-x

https://www.researchgate.net/post/Why-is-relativistic-thermodynamics-not-included-in-the-general-physics-textbooks-and-special-theory-of-relativity-textbooks

But most of these treatises look at the question trying to understand whether a body “looks hotter or colder” from the point of view of the other. My question has more to do with the intrinsic thermodynamic behavior of a process at relativistic speeds.

But really, the theory has to fit the data. So where are the data?

 

[Grasshopper]

This is interesting, but maybe not what you’re looking for. https://en.m.wikipedia.org/wiki/Relativistic_quantum_chemistryThe most interesting to me is the section on lead.

“Without relativity, lead would be expected to behave much like tin, so tin–acid batteries should work just as well as the lead–acid batteries commonly used in cars. However, calculations show that about 10 V of the 12 V produced by a 6-cell lead–acid battery arises purely from relativistic effects, explaining why tin–acid batteries do not work.”The citation is number 14.

 

[Nugatory]

Does diffusion occur more slowly in a container moving close to relativistic velocity? I guess doing this experiment is technically very difficult. But haven't we developed tools improved enough to allow this?

Don’t guess when you can calculate.

What is a reasonable mass for a container in which we might observe diffusion? Maybe 100 grams, .1 kg.
What is the maximum acceleration it can tolerate without breaking up? Something like 100g, which we is within the realm of possibility for a railgun.
So we’re going to use a railgun to accelerate a .1kg object at 100g until it reaches some relativistic velocity, something like .8c or thereabouts.

How long of a railgun do we need?
How much energy is required (assume 100% efficiency for simplicity)?

 

[hutchphd]

I'm a little confused as to what about diffusion might be interesting. How about studying the internal combustion engine relativistic speeds?
And why would you seriously propose substituting the cooling of a tank of water for a precision cesium clock as a measure of time. Better you use an hourglass.
As the OP suspects, none of this makes much sense.

 

[Ibix]

My question has more to do with the intrinsic thermodynamic behavior of a process at relativistic speeds.

It's easy to show that if one time measuring process appears to "run slow" so must all others and by the same factor, or else you can detect your absolute speed by comparing tick rates of two clocks. In other words, your question boils down to a test of the principle of relativity, of which there are many. See the experimental basis of special relativity FAQ linked in a sticky post at the top of the forum.