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from Part IV - States and the second law
Published online by Cambridge University Press: 05 June 2012
Interacting systems
We now examine interacting systems. We will find that the number of states for the combined system is extremely sensitive to the distribution of energy among the interacting subsystems, having a very sharp narrow peak at some “optimum” value (Figure 7.1). Configurations corresponding to a greater number of accessible states are correspondingly more probable, so the distribution of energy is most probably at the peaked optimum value. Even the slightest deviation would cause a dramatic reduction in the number of accessible states and would therefore be very improbable.
This chapter is devoted to developing this statement of probabilities, which underlies the most powerful tools of thermodynamics. We elevate it to the stature of a “law.” Even though there is some small probability that the law may be broken, it is so minuscule that we can rest assured that we will never see it violated by any macroscopic system. Rivers will flow uphill and things will freeze in a fire if the law is broken. No one has ever seen it happen, and you can bet that you won't either.
Microscopic examples
We now investigate some examples of how the number of states is affected by the distribution of energy between interacting systems. Consider the situation of Figure 7.1, where an isolated system A0 is composed of two subsystems, A1 and A2, which may be interacting in any manner.
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