Relativistic version of 2nd law of thermodynamics

In summary, the classical version of the second law of thermodynamics involves a definition of a system and the concept of entropy increasing over time. It also takes into account the idea of simultaneousity, where the state of the system is compared at different moments in time. There are generalizations of this law that are compatible with both special and general relativity, and can deal with systems in curved spacetime, situations without a defined direction of time, and systems in closed timelike loops. However, black holes must have entropy in order to satisfy the second law, as the increase in their entropy compensates for the decrease in entropy of the object being swallowed.
  • #1
Dmitry67
2,567
1
The classical version of that law includes a definition of a system and entropy increasing over time.

It uses a notion of simultaneousity - we compare a state of the whole system in different moments of time.

My questions:

1. Do you know any good SR-compatible generalizations of that law?
2. Are there any GR-compatible generalizations of that law which can deal with:
* systems is curved spacetime, where the direction arrow of time becomes more and more fuzzy.
* situations where no common (for the whole system) direction of time can be defined; for example, part of a system is orbiting a black hole while another part of it is falling inside;
* systems in closed timelike loops
 
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  • #2
Entropy is a Lorentz invariant scalar, so the second law is compatible with special relativity. If entropy is increasing in one frame, it is increasing in all frames. See "Relativity, Thermodynamics and Cosmology" by Richard Tolman for a discussion of the extension of thermodynamics to special and general relativity.
 
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  • #3
Just a sec, you are talking about the infinitely small systems? so like if law is satisfied in every point of spacetime then it is satisfied globally? I would agree, but then the following quote from Wiki:

If black holes carried no entropy, it would be possible to violate the second law of thermodynamics by throwing mass into the black hole. The only way to satisfy the second law is to admit that the black holes have entropy whose increase more than compensates for the decrease of the entropy carried by the object that was swallowed.

does not make any sense because we just follow the falling object inside the hole - and for that obejct everything looks normal een when it passes thru the horizon.
 

Related to Relativistic version of 2nd law of thermodynamics

1. What is the relativistic version of the 2nd law of thermodynamics?

The relativistic version of the 2nd law of thermodynamics states that the total entropy of a closed system and its surroundings will always increase in a natural process, even when taking into account relativistic effects such as time dilation and length contraction. This means that the overall disorder or randomness of a system will always increase over time, regardless of the observer's frame of reference.

2. How does the relativistic version of the 2nd law differ from the classical version?

The classical version of the 2nd law of thermodynamics only applies to non-relativistic systems, where time and space are considered to be absolute. In contrast, the relativistic version takes into account the fact that time and space are relative, and that different observers will measure different rates of entropy change. Additionally, the relativistic version allows for the possibility of negative entropy change in certain scenarios, which is not allowed in the classical version.

3. Can you provide an example of the relativistic version of the 2nd law in action?

One example of the relativistic version of the 2nd law of thermodynamics is the decay of subatomic particles. In this process, particles with higher mass and energy decay into particles with lower mass and energy, ultimately increasing the overall entropy of the system. This process is governed by both classical and relativistic laws, but the relativistic version takes into account the changes in mass and energy as observed by different observers.

4. How does the relativistic version of the 2nd law relate to the theory of relativity?

The relativistic version of the 2nd law of thermodynamics is derived from the principles of the theory of relativity, which states that the laws of physics must hold true for all observers, regardless of their frame of reference. By incorporating the effects of relativity, the 2nd law is able to accurately describe the behavior of systems in different reference frames and at high speeds.

5. Are there any practical implications of the relativistic version of the 2nd law?

Yes, the relativistic version of the 2nd law has important implications in fields such as cosmology and astrophysics, where relativistic effects are significant. It also plays a role in the development of technologies such as nuclear reactors and particle accelerators, where the understanding of entropy and energy transfer is crucial for efficient and safe operation.

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