热场中熵与温度孤子

ENTROPY SOLITONS AND TEMPERATURE SOLITONS IN THERMOFIELDS

证明熵Ｓ（ｘ）和温度Ｔ（ｘ）为∞＾２ｎ维辛流形Ｔ＾＊Ｍ上的一套正则坐标，热场系统由Ｈａｍｉｌｔｏｎｉａｎ Ｈ描述。对于热传导情形，Ｈ＝－∫ｄ＾ｎｘλ△↓Ｓ·△↓Ｔ．当热传导系数λ分别取λ１＝Ｔ＾２－１，λ２＝ｓｉｎＴ，λ３＝１＋ｃｏｓＴ，λ４＝１－ｃｏｓＴ等温度的函数时，Ｈａｍｉｌｔｏｎｉａｎ运动方程给出温度孤子分别为Ｔ１＝ｔｈζ，Ｔ２＝ｃｔｈζ，Ｔ３＝２ｔｇ＾－１ｅ＾ζ。

It is proved that entropy S(x) and temperature T(x) are a set of canonical ccordinates on the ∞2n-dimensional symplectic manifold T* M. For the case of thermal conduction,the Hamiltonian of the system is given as When the thermal conductivity λ takes the values, respectively, λ_1=T2-1, λ_2= sin T, λ_3= 1 + cosT, λ_4 = 1- cosT and so on,the Hamilton's equations possess the temperature soliton solutions T_1 = th, T_2 = cth T_3 =2tg￣(-1), T_4 = 2ctg ￣(-1) and others, where= ( x, y, z ) is a function. Similarly, the theory leads to some entropy solitons. The physical meanings of these solitons are simply discussed.