Gambling and Law Zero

Heat flows from regions of low coldness to high coldness BY CHANCE. In fact, we now know that coldness (another word for the reciprocal of the absolute temperature) simply measures the bits of uncertainty S about the state of a system gained per unit of thermal energy E added thereto, i.e. the uncertainty slope dS/dE. On average for most macroscopic and spin systems this uncertainty slope decreases as one adds energy. A little math will show [CAN YOU DO IT?] that the most likely distribution of energy (or any conserved quantity) between two systems, if there is one, is a distribution for which the individual system "uncertainty slopes" are the same. If not, energy flow from low to high slope systems opens the door to a wider range of random choices. A zeroeth law with teeth then follows.

I've been working with Saunders College Publishing to prepare a supplement on this subject for the year 2000 edition of Serway and Beichner, a top market-share calculus-based university introductory physics text. An early outline of this supplement can be found here. Comments and suggestions (e.g. on making supplements like this clearer and more easily accessible) are invited.

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