1

In relativity, we define proper time for a particle therefore can discuss about casuality-order of events preserved for it. For statistical mechanics in classical mechanics, macroscopic systems evolving by time follow the same time axis-hence the increase of entropy by time(a.k.a. the second law of thermodynamics) can be accepted 'naturally'. However, for a macroscopic system in equilibrium, can we define proper time? For example, for gases, if the comoving frame of the particles differ, the particles themselves can evolve through their own proper time-however what about the gas, the macroscopic system itself? Is there a well-defined time describing change for equilibrium statistical mechanics?

p.s.) The anomaly in definition of temperature in special relativity also led me to this frustration.

Source: http://kirkmcd.princeton.edu/examples/temperature_rel.pdf

Thank you for reading my question. If you have a clear answer, I would appreciate it if you let me know.

Jiwoo Hong
  • 13

1 Answers1

1

Every macroscopically large box of gas that is not accelerating has a well-defined rest frame of reference and thus the proper time of that box of gas will be equivalent to the coördinate time in that rest frame of reference in Special Theory of Relativity.

There is no generally accepted solution if the box of gas is moving. Plenty of authors have argued their case, but you have those that argue it is going to transform by multiplying the Lorentz factor $\gamma$, others argue it should be a division, yet others say it should be Lorentz invariant, and some others entertain the square of the Lorentz factor in either multiplication or division. My personal belief is that temperature is simply only well-defined for systems at rest.

In General Theory of Relativity the concept is worse and I am not familiar with attempted solutions.

naturallyInconsistent
  • 14,919