# Maximal Entrop, Temperature & Energy Transfer

1. Sep 11, 2010

### azaharak

Hope you can help my understanding.

Looking at entropy from a stat mech standpoint,
two systems brought together will result in a higher entropy system.

According to Kittel, the most probable configurations will dominate the statisical properties of the combined system, most probable confiigurations are ones that maxmimize the entropy. (pg 36 Thermal Physics Kittel).

For large systems, the multiplicity function or degeneracy is sharply peaked.

The direction of transfer of thermal energy is governed by what situations maximize entropy.

Is it possible to conceive two very small systems (N small), where thermal energy is transfered from the colder system to the hotter system.

I'm thinking that for small systems, it is conceivable that maximal entropy occurs for thermal energy transfering from a cold object to a hot object.

I have also though that this would be the analoge of a two particles colliding, a fast moving one and slow moving one, where the slower particle looses energy in the collision and the faster particle gaining energy.

Thanks

Az

2. Sep 11, 2010

### Andy Resnick

3. Sep 11, 2010

### azaharak

I'm not sure how that relates to the gibbs paradox

My understanding of the gibbs paradox involves the indistinguishability of particles, a quantum correction.

I can read straight out of Kittel Page 45.

"We can show that the total entropy always increases when two systems are brought into thermal contact."

but this is not answering my original question

Thanks

4. Sep 13, 2010

### Dr Lots-o'watts

A fast particle moving in the y direction, being hit by a slow particle in the x direction, is such a collision. I think it is possible for a small fraction of collisions to transfer heat in such an inverse manner. However, in a closed system, this only increase the thermal gradient, which in turn increases the probability of collisions in the regular sense. The possibility of such a collision is non-zero, but negligible. This is "statistical" mechanics after all.

5. Sep 14, 2010

### Andy Resnick

Fair enough.

Ok, your question regarding microscopic violations to the second law of thermodynamics, is allowed by the fluctuation-dissipation theorem and has been experimentally demonstrated:

http://prl.aps.org/abstract/PRL/v89/i5/e050601