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A fascinating result of the last model is the connection of the thermodynamic state function entropy to notions of probability. The second law of thermodynamics is really nothing more than an expression of the probability of certain configurations occurring in multiparticle systems. In most of the examples you worked out in discussion/lab and in the homework, the number of particles was fairly small. In these small-number-of-particle examples, you could actually calculate probabilities of different configurations of a system. You found that the configurations that were not the most probable still had values that were significant. The system would actually find itself in these less probable configurations some of the time. When we focus on real macroscopic samples of matter, the number of particles gets to be the order of Avogadro’s number. Now the probability of a system not being in the most probable configuration is vanishingly small. It is because we always deal with systems in everyday experience that have $$10^{20}$$ or more particles, that we can make absolute statements like, “heat always flows from a hotter object to a cooler object.” It is not that some fundamental law of physics would be violated (conservation of energy, for example) if we sometimes ran across an interaction in which energy was transferred from the cooler to the warmer system as heat. It is just that the probability of this happening is so small, it would never be observed, even if we waited and watched for the entire age of the universe. The probability is just that small!