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For gravitational systems one has to be careful making statements about entropy and the second law of thermodynamics. Your example is similar to the gravitational collapse of a gas cloud if you think carefully about it. In that case and in yours, the shrinking of the gas will raise it's heat. Now even though the increase of entropy due to the increased ...


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I learned I can calculate the entropy $$S=-k_B\sum_jp_jln(p_j)$$ where $$p_j$$=probability at j state but I saw that the entropy is also can be calculated by $$S=-k_Bln(Z)$$ I think this equation applicable for both of isolated system and non isolated system these two equations are same ? Given the number of states $\Omega(E,\Delta ...


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The answer is no. Once a black hole is formed you no longer have access to the information stored inside it. The information is not lost, but slowly radiated away as the black hole evaporates. So, the ideal system would be one that is almost near the density for a black hole collapse, but never reach it. Otherwise you loose "easy" access to the information ...


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All energy transfer in an (ideal linear) electrical circuit is a form of work. Its just moving charges in electromagnetic fields. Resistor transfer energy to something external to the circuit, and often this energy will end up dissipated as heat in the surroundings. Inductors and capacitors, however, simply store energy and then release it again. Work is ...


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If you put a gas in a box and wait for it to reach equilibrium, then a) its full behaviour then is described by equilibrium statistical mechanics and b) it will remain in this state - as described by equilibrium statistical mechanics - forever (really forever) if nothing is done to it. The key point is that, although it carries "equilibrium" in it, ...


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One may still describe the behavior of such a system at maximal entropy using a theory that does use the concept of time, or the time coordinate $t$. But it is true that operationally speaking, the passage of time ceases to exist because the equilibrium associated with the maximum entropy is incompatible with the existence of thinking observers. Note that ...


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It is important to distinguish between the time and the flow of time. The time, $t$, is just a coordinate like $x$, $y$ and $z$ that we use to specify points in spacetime. The time coordinate doesn't have an arrow any more than $x$, $y$ or $z$ have arrows. The time axis has a negative and positive direction, just like the spatial coordinates, but at normal ...


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The gas could fall into a state of low entropy randomly. It is important to remember that the laws of thermodynamics are probabilistic, and they say not what will happen but what usually will.


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To answer your question first we need to know why do we need quantum mechanics in thermodynamics: In Quantum mechanics you can attribute a wave function(to be precise wave-packet) to a particle. . At high temperatures particles can be pictured as billiard balls because their size is much smaller compared to interparticle distance. But as the gas cools down ...



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