解 本题的思路与上题完全相同. 我们以玻色子和费米子组成的系统为例. 当系统含有[tex=0.857x1.0]+NBI8Pm2vVS+bGgOpHKyOA==[/tex]个玻色子, [tex=1.143x1.143]ziGcoHaek+CPS/FeGW3BxA==[/tex]个费米子,总能量为[tex=0.786x1.0]I/kNMtd8YcgkWCrgriW/hA==[/tex],体积为[tex=0.643x1.0]jro2X/cRz2SsmjZvcOdvsQ==[/tex] 时,粒子的分布[tex=1.786x1.357]IWPJjnhl8c2oO87/g20OAI5YjtGRUwDeNBKIgQN3HOg=[/tex]和[tex=1.786x1.429]18VHbN8mGsCyyxVdXHxshExBeZxDgkI2LPYqyZXVKIU=[/tex]必须满足条件[tex=9.571x8.643]rZM5/OPAdr7aX+kNl9iwpIU8GWdM0MAyIn0SZ4C8Vynxkc+LdKzQDLDU5Zmv9B3fLrkfrdBDC5Owz9EwfE2nHn2AnDwd6ty6EooPlyWImuheCQYU/1bRh+bnBLV8VmB1iqC3hY/cV3o5C7q/+dFQFKpAOcr55knt3/klM/fBo+s/uHAWBbZxkI+vcee5rEp3Dql1eI/q3hGRGTr+J14d/Db/bjWn7XCTv/Bu5aHxc+Q=[/tex]  (1)才有可能实现.玻色子处在分布[tex=1.786x1.357]IWPJjnhl8c2oO87/g20OAI5YjtGRUwDeNBKIgQN3HOg=[/tex],费米子处在分布[tex=1.786x1.429]18VHbN8mGsCyyxVdXHxshExBeZxDgkI2LPYqyZXVKIU=[/tex]时 ,其微观状态数分别为[tex=9.429x6.357]rZM5/OPAdr7aX+kNl9iwpHSzAKHKwwwfHe0nedgReCxnBs5YBH30u7emthJS8kXoYXjtUFsChpJh/H4Y7Y/KAFIn07IfUq2HQC9YkBgoY2syvu257TNYmuUxEwEkuxKbjRnQRwwsa0nCb0b62v0Mh4jscN7qnBjzThAOKJaun5pEX7LiXMKFJPPFZPj0EyKiw/s0xL1Nq7rUzpAcy2nDEoQOXLz/ZnrbQ/gxKa/q5wmzy8NICTsQdB7G29u8AUJJATHVyEFKiYd+udfFgu779qZwSPkbtPBCfMUONmXZbf2v2K7l4u/FsD0OkitMWWBtFk3a7wn0S1M93EJ+t0CarA==[/tex]  (2)系统的微观状态数[tex=1.714x1.286]hZTSo/SQ/iZG/8p112upmA==[/tex]为[tex=4.429x1.286]6H1T77EkSsG5ZXHIEsg8r59FSRTVClKKG1yDbwi3zYpBAaoaiiKk1/9VkNSdHY3k[/tex]  (3)平衡状态下系统的最概然分布是在满足式 (1)条件下使[tex=1.714x1.286]hZTSo/SQ/iZG/8p112upmA==[/tex] 或[tex=2.714x1.286]ydd/nVO1SBD4gQsCNN8WV/gKRWTL1bIuU3sfjxlUmwqnWUpToJrFlOe3k4+q/6wd[/tex]为极大的分布. 将式( 2)和式( 3) 取对数,利用斯特林公式可得[tex=21.571x5.786]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[/tex]令各[tex=0.786x1.0]+9P6IoZVDt3Advj56enSUg==[/tex]和[tex=0.786x1.429]II3zmNU1HvGKytR3Gf7op4CsrhTDhtsXt7A78X2TXSM=[/tex]有[tex=1.214x1.214]OQ3Sm89m/htnC16qFT5aLw==[/tex] 和[tex=1.214x1.429]vGkqHtSr3HhllJ3zH7HrRPO0pgTBVFFcPt8rtaKgNWc=[/tex]的变化, [tex=2.714x1.286]8i9SCE2nGNZSQns6avIxTdJDI9OLgZyzmCLM19hnAoU=[/tex]将因而有[tex=3.286x1.286]rqQEhWAyAe8HnBRSgc9R9AwsKkLw9f3qZGeh7S9tdQE=[/tex]的变化,使[tex=2.714x1.286]8i9SCE2nGNZSQns6avIxTdJDI9OLgZyzmCLM19hnAoU=[/tex]为极大的分布[tex=1.786x1.357]IWPJjnhl8c2oO87/g20OAI5YjtGRUwDeNBKIgQN3HOg=[/tex]和 [tex=1.786x1.429]xzsfc1xdwOpb2Cgb2dI5XaUvhZ9oEn+e8ioLSn8ZeG4=[/tex] 必使[tex=4.857x1.5]rQOmS+Hx4poyZfY0RL47ur9cW52ALXeqARXBArDlwVYy5Fsz0UIbUOIM6C3Pyc6o[/tex]即[tex=19.357x4.5]qeiYnKXLEhyhuGRg8yLtr0kC/YM3Zn0DgLdUtGiJvrVUspq9qdsPYCKjDIcUB+K1Z+3hyLcMvSOpEY8lGxHIaTWP4x7MZZBz3aaLPikEjauxnj+LTNfPOv2ejxzsbibSbN2Ga3Hb6+v8SzXXfh8md1hUukRaS+IRWOuNZxENQmmigyolCsdQ3vvblzUbL8OcH/2F7M1XvB6t44eTFXIhW7DJjYLrxLRi2mSKh6THb8MKyGXb6QE/5I/vvybg5/uy9zO+8mgwldD5KaCOcJypwqwVasAGdL2OzgQtXpSoJvAObzPv0aM0B1esfpMySzqr[/tex]但这些[tex=1.214x1.214]OQ3Sm89m/htnC16qFT5aLw==[/tex]和[tex=1.214x1.429]vGkqHtSr3HhllJ3zH7HrRPO0pgTBVFFcPt8rtaKgNWc=[/tex]不完全是独立的, 它们必须满足条件[tex=12.357x8.643]rZM5/OPAdr7aX+kNl9iwpBdN3WtRIBxS+7PnOLiSs1jFt9uIjHgL5XFMC1KGVtO99d8eq3JfiKFsXoYG6Xpp+IZvoWWqMptVOLMOWE+zzlhUx7l2Sy0AuATNSPMAxXIz8d+krt/bCsy/zeYWaKXWcJKozEi4tDTtZC5snhclJRRO6t4U8GeNtA9sazOU7n3ZOQRlagUxSR5I3x1bzZK43Lko5iY1naDe6ZDGI7HXKYabB9F7zu9vIN/+e8rBrbv8RMWP1RUuFzDucJGG5QKaP/KOwxOCFfYd0oaULHwndYJXA1A7bdnlGtEY4+pCm94p[/tex]用拉格朗日乘子[tex=0.643x0.786]KFl4ILVOU0DB1zdU6Y+zcg==[/tex] 、 [tex=0.929x1.143]g+5FJkfRy0srLm2sAB0jHBEtO9QVmQNl7jVKaXvezFs=[/tex]和[tex=0.571x1.214]CyLt5nwVs0oLAbCn8AssqQ==[/tex]分别乘这三个式子并从[tex=3.286x1.286]rqQEhWAyAe8HnBRSgc9R9AwsKkLw9f3qZGeh7S9tdQE=[/tex]中减去,得[tex=11.714x1.5]rQOmS+Hx4poyZfY0RL47ui33K1caw9QTXXOk5mu3p6OKb53s9KRPbLT1hRHSs80jX/JvTMyqi2y5sqej4g6qYau1bVElJGbvAuuvL58UBKCJLIS21PTlHhZAduAJz6G3[/tex][tex=13.429x7.5]qeiYnKXLEhyhuGRg8yLtr8L6JPmvmIShhybTcGpGpRVl4HV/6Jv4snqDUzRJHiKzYVYBir+jW1UTMQZbBWJa9LgLJStbCgLoI3bmWx925Wmea8LbRlp8RShlMTBCmO45IEuQ/qWeIpALnIWJ53xaZJrnQL7DKen2tvHYS+g7fEgmCx8fuA5sAgpaYL1vxTQ+0oGon/iJSDMmqwlWz2XEumMUT4u7gZDzkmu52aCu3oQGB2PrGejbLRtC9eyDAZH/kjMwxuxTCyQSrfvXRrCn0hyJ4AkARhpOu2T7rcoHUTq4w9PPG0fGM1yJKaYhsYLQ8pk3qMIzyJt3Rv5osIOJOefr0D0cmGuqB1f//4donijNmsjCciNXJI27Ubwv/CHowKfhpIXCNOpagAdQP+BvrawuQuBxCnurgv7pkQls5Jw=[/tex]根据拉格朗日乘子法原理,每个[tex=1.214x1.214]OQ3Sm89m/htnC16qFT5aLw==[/tex]和[tex=1.214x1.429]vGkqHtSr3HhllJ3zH7HrRPO0pgTBVFFcPt8rtaKgNWc=[/tex]的系数都等于零,所以得[tex=10.857x5.643]rZM5/OPAdr7aX+kNl9iwpCP3BSrSm7i6ZKwIgE3LSTX/uQp7AQJbB28ti1gQgRMbtzypHyl3q0fzkx0Ke2NNAg1PL4c+IjjnNQ6RPrHOolozcCoWyaD7HzMIR9oE5Ej3gCRz0LQpWQgAiUH1tW0UO2NWR9cRmoRhSCqRe7z6QOYTMuMDd3rOGG/ds7tnOyhMPW2gDr7WfZFM5HtlpU3PGXc2NBy1aIFPmxX1sefMOTkUwTbuwyRbuwErN5Sbe2Uf5m4WEQD0UrF8b0bA4VFTdiHVe0PUqPSAKUAk9lHJSp8=[/tex]即[tex=5.571x2.214]5oTvdhOINIMNi0B1oPp2hAUek5U5gwX8JHeUVhuA//Qi5MQwPwXfWEsPc5snMvpMeyD5jcdM/U5cTmDpClAmIA==[/tex]