Karl Popper on brownian motion and the 2. law of thermodynamics

[LTP]

I'm reading an old, maybe outdated, paper by Karl Popper about the 2. law of thermodynamics, brownian motion and perpetual motion.

Popper writes:

According to Einstein's theory we are forced to say that in the Brownian
movement, observable heavy particles are sometimes lifted against the
gravitational field of the earth, at the expense of a (slight) cooling down of
the liquid. Of course, just as many particles are sinking, thus restoring the
lost heat. But this does not matter : the letter of Planck's law is undoubtedly
violated, as Einstein in fact stated.
This situation is a little more serious than is usually seen. For the now
generally accepted theory of the Brownian movement clearly implies
that, precisely as small fluctuations affect small suspended bodies, big
fluctuations will affect big suspended bodies ; and it implies, moreover,
that big fluctuations, although very improbable and therefore very rare,
must occur, precisely as small fluctuations must occur.
All this is of course very well known to every physicist ; and I believe
that most physicists will accordingly agree that the entropy law, in Planck's
formulation, is simply falsfied by the Brownian movement, as interpreted
by Einstein. However, they may say, perhaps, that the Maxwell-Boltzmann
law is certainly not falsified but supported by Einstein. This is quite correct.
But the following consequences have not, apparently, been drawn from
the situation which I have described.

Before that, Popper has described Planck's law as:

There does not exist a perpetual motion machine, of the second
order, that is to say, a physical system, immersed in a heat bath, which,
by cooling down (or, which is the same, by absorbing heat from the
surrounding heat bath), can move a heavy body against a force, thus
increasing its potential energy ; or in terrestrial terms, a machine which,
by cooling down, can lift a weight.

So, my question is: Is brownian motion considered to be a violation to the 2. law of thermodynamics today? To me, it sounds like Popper is doing a lot of hand waving; and not so much with content in it.

Se the attachment for the full article.

 

[Andy Resnick]

No, Browian motion is not incompatable with entropy increase. Feynman invented a nice puzzle- a brownian ratchet which can appear to raise a macroscopic weight, driven by brownian motion. The resolution to this puzzle is interesting, and the groups trying to understand actin polymerization in terms of a Brownian ratchet would do well to read it.

The Second law of thermodynamics is a law of thermodynamics, and thus is a macroscopic, time-independent formulation. It has been experimentally demonstrated that entropy can decrease spontaneously for short times in out-of-equilibrium systems, in accordance with the fluctuation-dissipation theorem.