Relative Entropy: Coffee Hot after Acceleration?

[Fumarium]

If I was sitting in my office holding a hot cup of coffee, then suddenly accelerated to close to the speed of light for say 5 minutes of my time, then decelerated to my previous velocity, wouldn't my cup of coffee still be hot? Since only 5 minutes of my time has passed? Even though 60,000 years of my office's time has passed? Doesn't this mean that entropy is relative to velocity? And if the rate of our Universe’s expansion speed is INCREASING - does it correlate then that its entropy is DECREASING?

 

[The riddler]

This doesn't mean that entropy is "decreasing", when you are traveling at close to the speed of light you have increased entropy slower than the universe around. While going at this speed 5 seconds to you could be 60,000 years to your office, meaning that the universe has gone on longer so entropy for the universe has seemed to have gone faster in comparision to you. So your right, entropy is relative to velocity but that is only because velocity is relative to time (through einsteins physics) and time is relative to entropy.

Thus the entropy of the universe is always increasing but the rate inwhich it increases will change with time. For example, right now with all the stars burning the universe is gaining entropy quickly while the universe may be gaining entropy slower in 100 trillion years because the energy and matter in the universe will be more spread out.

Hope this answers your question.

 

[Civilized]

Doesn't this mean that entropy is relative to velocity?

Entropy is an observant dependent quantity, just like kinetic energy, etc this does not make the concept meaningless.

And if the rate of our Universe’s expansion speed is INCREASING - does it correlate then that its entropy is DECREASING?

No it doesn't, maybe you could describe in detail a particular observer in a particular state of motion and why you think the accelerating expansion of the universe would cause a decrease in entropy? Keep in mind that the accelerating expansion of the universe is very different then accelerating away from your office chair.

 

[Vanadium 50]

If I was sitting in my office holding a hot cup of coffee, then suddenly accelerated to close to the speed of light for say 5 minutes of my time, then decelerated to my previous velocity, wouldn't my cup of coffee still be hot? Since only 5 minutes of my time has passed? Even though 60,000 years of my office's time has passed? Doesn't this mean that entropy is relative to velocity? And if the rate of our Universe’s expansion speed is INCREASING - does it correlate then that its entropy is DECREASING?

None of that follows from the premise.

 

[lifeson22]

Entropy is a measure of the probability of finding a system in a given configuration - period. You might have seen it in your statistical physics or thermodynamics textbooks as:

S\proptolog(g), where the g is the multiplicity of the system's configuration, given by the binomial distribution for a system of N particles of type A or B:

g=\frac{N!}{N_{A}!N_{B}!}

An isolated system will always progress to a state of highest probability - and thus highest entropy by our definition - because the slightest deviation from equilibrium puts the system in a far less probable configuration.

You're right that something special happens after a hyperspeed trip with your cup of coffee. Moving near the speed of light distorts the space-time continuum, so that five minutes to you is eons to somebody else. If your coffee is not perfectly insulated, heat will dissipate from it and reduce its entropy at the expense of the entropy of its surroundings (which increases) - and this progresses at a rate determined by the gradient of temperature between coffee and surroundings. It's a time dependent process, and because you've been flying at hyperspeeds, the time required for your coffee to cool off will be different from the time measured by somebody sitting in your home planet.

It's not that entropy is velocity-dependent, it's that time is velocity dependent. If you see the process move along a lot faster than a stationary observer, it's because time *IS* moving along very differently for the both of you, not because entropy is taking on different values for both of you.

 

[Andrew Mason]

If I was sitting in my office holding a hot cup of coffee, then suddenly accelerated to close to the speed of light for say 5 minutes of my time, then decelerated to my previous velocity, wouldn't my cup of coffee still be hot? Since only 5 minutes of my time has passed? Even though 60,000 years of my office's time has passed? Doesn't this mean that entropy is relative to velocity? And if the rate of our Universe’s expansion speed is INCREASING - does it correlate then that its entropy is DECREASING?

The cup of coffee would cool in less than five minutes because it would be all over your shirt in the first few seconds. Given the acceleration that would be needed if you were going to do this trip in 5 minutes, local time, you would not feel the scalding hot coffee on your skin because your brain would have exploded from the pressure.

I have a copy of a copy of a book on Relativity and Thermodynamics by Richard Tolman. You can download the chapter on "[URL - Relativity-Thermodynamics_Ch_V.pdf"]Relativity and Thermodynamics here[/URL] if you are interested. It is an old book but (relatively) easy to read.

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