# Questionning the secong law of thermodynamics

#### fluidistic

Gold Member
Hi PF,
I'll be soon seeing the second law of thermodynamics in my physics course so I didn't grasp it yet.
But I've read in the French wikipedia :
Le célèbre mathématicien Henri Poincaré démontra en 1890 un théorème extrêmement général, dont l'énoncé physique est : « Tout système macroscopique repasse une infinité de fois aussi près que l'on veut de son état initial. » Ce « théorème de récurrence » fut opposé au second principe, car il implique que toute évolution macroscopique est réversible. Pour contrer ce théorème apparemment inattaquable, Boltzmann calcula le temps nécessaire à 100 cm3 de gaz pour revenir à son état initial. Il trouva 10^{(10^{10})} années !!! Autant dire que, si le problème des cycles de Poincaré subsiste, il n'est pas d'une urgence brûlante
It means that Poincaré demonstrated a theorem in 1890 which says "all macroscopic system will be an infinite number of times as close as we want to its initial state". Then it follows " This recurrence theorem was opposed to the second principle of thermodynamics because it implies that all macroscopic evolution is reversible. To counter this theorem Boltzmann calculated the time necessary for $$100 cm^3$$ of gas to return to its initial state to be $$10^{10^{10}}$$ years. Then it says something like "IF Poincaré's problem still exists, it's not of a big matter".
But reading the paragraph we can see that the "IF" shouldn't be here. It's clear that it's a problem for the 2nd principle of thermodynamics. So my question is "Is the second principle of thermodynamics right?". In any case I'd like to see clearer if you can help me... Thanks.

#### DeShark

I believe that the problem as stated by Poincaré is only a problem if you use the traditional viewpoint of thermodynamics. After the development of statistical mechanics and its links to entropy, it is seen that the second law is only a probabilistic law. All of the molecules in a gas could, in theory, move to one half of a container spontaneously, leaving the other half empty. However, as Boltzmann points out, the chances of this are extremely small, such that it's not a problem. If you take the statistical point of view, the second law is only a very very good approximation.

Je crois que le problème annoncé par Poincaré n'est qu'un problème lorsqu'on utilise le point de vue traditionnel de la thermodynamique. Après le développement de la physique statistique et ses liens avec l'entropie, on voit que la deuxième loi n'est qu'une loi probabiliste. C'est possible, théoriquement, que tous les particules dans un gaz peuvent se déplacer dans une partie d'une boite spontanément. Cependant, Boltmann a bien noté que la probabilité de telle circonstance est vraiment petite et donc ce pose pas de problème. Si on prend la point de vue statistique, la deuxième loi n'est qu'une très très bonne approximation. (Excuse any errors in my french, it's not my first language)

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#### fluidistic

Gold Member
Thanks a lot. So the second law of thermodynamics is not wrong but not 100% precise as any other theory I think.
Your French is good by the way.

#### DeShark

Exactly, it is a general principle rather than a law. But it works extremely well and is really the only way of dealing with systems with so many degrees of freedom.

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