Relativistic version of 2nd law of thermodynamics

Dmitry67

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

dx

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.

Dmitry67

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:

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.