# do relativistic velocities change the apparent entropy content of the moving object?

Imagine a box of hot gas. It has a certain (large) amount of entropy, which we can relate to the amount of information needed to completely specify the position and velocity of every gas particle in the box. Attach a clock and rocket motor to the box and accellerate it to close to the speed of light. As the rocket zooms past us, we notice that the hands on the clock it carries are seemingly frozen, and with some special apparatus we notice that the gas particles themselves do not seem to be moving either. Furthermore, the length of the box in the direction of travel has apparently vanished, rendering the box two-dimensional. The amount of information needed to completely specify the contents of the box is reduced, because 1) the box is missing one degree of freedom it had while at rest (relative to us) and 2) every one of the gas particles now has exactly the same velocity, say .99999c in the direction of travel, and their positions within the box itself are no longer changing with time. It would seem then that the box as observed from a nonmoving reference frame now contains less entropy than it did while at rest in that frame. (An observer attached to the box would detect no such changes in it.) What is wrong with my understanding of this?

• the box is missing one degree of freedom it had while at rest (relative to us) no... every one of the gas particles now has exactly the same velocity, say .99999c in the direction of travel, and their positions within the box itself are no longer changing with time. and no. Commented Feb 9, 2014 at 22:05
• Proving the Lorentz invariance of the entropy and the covariance of thermodynamics gives a very clear treatment of the foundations of relativistic thermodynamics and the fact that entropy is a Lorentz scalar (for both classical and quantum systems). Commented Aug 1, 2023 at 21:28