Thermal State in Relativity Theory: Can It Happen?

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Discussion Overview

The discussion revolves around the concept of thermal states in the context of relativistic physics, particularly focusing on whether a system of colliding particles can reach a thermal equilibrium analogous to classical thermodynamics. Participants explore the implications of relativistic effects on temperature measurements and the definitions of thermodynamic quantities in different reference frames.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether a system of many small hard balls, colliding at velocities greater than c/2, can converge to a thermal state similar to that described by the Maxwell-Boltzmann distribution, and whether relativistic corrections are necessary for different observers.
  • Another participant references the Maxwell–Jüttner distribution as a relevant concept for relativistic thermal states.
  • A subsequent post suggests that there exists a stationary or asymptotic thermal state for a system of neutral particles in the relativistic regime, seeking confirmation of this idea.
  • One participant affirms the existence of such a thermal state.
  • A question is raised regarding the temperature measurement by an observer in a moving reference frame (S') for a gas sample that is static in the lab frame (S), specifically whether the observer measures the same temperature T after accounting for drift velocity.
  • Another participant discusses the historical context of thermodynamic quantities under Poincare transformations, mentioning contributions from notable physicists and the current understanding of defining quantities like temperature and entropy density as scalars in Minkowski space.
  • The role of quantum statistics and many-body theory in deriving thermodynamic quantities is highlighted, emphasizing the importance of the one-particle phase-space distribution function.

Areas of Agreement / Disagreement

Participants express varying viewpoints on the existence and definition of thermal states in relativistic contexts, with some affirming the possibility while others raise questions about the implications and measurements in different reference frames. The discussion remains unresolved regarding the specifics of temperature measurements and the definitions of thermodynamic quantities.

Contextual Notes

There are limitations regarding the assumptions made about the behavior of thermodynamic quantities under relativistic conditions, and the discussion does not resolve the complexities involved in defining these quantities across different reference frames.

DaTario
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TL;DR
If hard balls start colliding in such a way that most of them have velocities near c, is it possible to speak of a thermal state in the Maxwell- Bolstzmann sense?
Hi All,

Considering a set of many many small hard balls which start colliding inside a box. The velocities of these balls being mostly greater than c/2. Is it possible, in this case, to speak of convergence to a thermal state in the same sense of ordinary thermodynamics (i.e., using Maxwell-Bolzmann distribution)?
Are there any relativistic corrections for different observers?

Best Regards,
DaTario
 
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Thanks to you both.

So it seems to be correct to say that there exists, in the relativistic regime of a system with many many neutral particles, a stationary state (or perhaps an asymptotic state) which can be called the system's thermal state (having thus a given temperature T associated with it). Is it?

Comment: I have read partially these materials and it have become clear that there exists a probability density for ##\gamma##, which depends on the velocity. So the answer to my question above seems to be yes. I am just searching for a confirmation.
 
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Yes.
 
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Thank you, Orodruin.

In this respect, considering a reference frame S' with velocity v (near c) wrt the lab's reference frame S, when an observer in S' "sees" a typical gas sample whose volume is static in S and have temperature T also in S, does this S' observer measure the same temperature T (although a drift velocity v must be taken out)?

Best wishes
 
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That's a very good question, and the issue of the behavior of the thermodynamic quantities under Poincare transformations has been a decade-long debate between eminent physicists. Planck was among the first who worked on it and gave one partially consistent picture. A better solution has been found by Ott.

Nowadays we work with manifestly covariant quantities, i.e., with tensors in Minkowski space (including scalars and vectors and the corresponding fields of course; in QT the proper orthochronous Poincare group is substituted by its covering group which means to substitute ##\mathrm{SL}(2,\mathbb{C})## for the proper orthochronous Lorentz group ##\mathrm{SO}(1,3)^{\uparrow}##, and then also spinors of various kinds are added to the theoretical toolkit).

Today we define (sic!) quantities like temperature, chemical potential, internal energy density, entropy density,... as scalars. As with mass one simply takes over the definitions from non-relativistic physics in the local restframe of the medium. For details see

https://www.physicsforums.com/kbibtex%3Afilter%3Aauthor=van%20Kampen: https://www.physicsforums.com/kbibtex%3Afilter%3Atitle=Relativistic%20thermodynamics%20of%20moving%20systems , https://www.physicsforums.com/kbibtex%3Afilter%3Ajournal=Phys.%20Rev. https://www.physicsforums.com/kbibtex%3Afilter%3Avolume=173(https://www.physicsforums.com/kbibtex%3Afilter%3Anumber=1), https://www.physicsforums.com/kbibtex%3Afilter%3Apages=295, https://www.physicsforums.com/kbibtex%3Afilter%3Ayear=1968
http://dx.doi.org/10.1103/PhysRev.173.295
Everything, of course, derives also from (quantum) statistics and thus (quantum) many-body theory and coarsegraining of the microscopic dynamics to macroscopic observables. In this process the one-particle phase-space distribution function plays an important role (e.g., in the Boltzmann transport equation), and accordingly to the above strategy the phase-space distribution function is a scalar field. For details, see

https://itp.uni-frankfurt.de/~hees/publ/kolkata.pdf
 
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Thank you, Vanhees71!
 

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