Consider the system where $N_{A}=N_{B}=1000, U=5999 \varepsilon$ (see figure T2.6). Suppose that we can measure each object's energy to within $0.01 U \approx 60 \varepsilon$ (the size of one bin). Once the system has reached a macropartition in the most probable bin, it will never spontaneously move to a macropartition outside that bin.

Question

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Even in the most probable macropartition, there is always a non-zero probability, albeit very small, for the system to fluctuate to a less probable state due to the inherent statistical nature of thermodynamic systems. These fluctuations mean the system can spontaneously move to a macropartition outside the most probable bin, although such events are rare.

Consider the System Where NA=NB=1000,U=5999εN_{A}=N_{B}=1000, U=5999 \varepsilonNA​=NB​=1000,U=5999ε (See Figure T2 0.01U≈60ε0.01 U \approx 60 \varepsilon0.01U≈60ε

Consider the System Where $N_{A}=N_{B}=1000, U=5999 \varepsilon$ (See Figure T2 $0.01 U \approx 60 \varepsilon$