辛热力学原理

THEORY OF SYMPLECTIC THERMODYNAMICS

设2n维辛流形T*M的局部坐标为力学正则变量(q,p),定义T*M的2s维子流形T*N的两套坐标分别为热力学变量(X,Y)和(S,T),则从力学变量到热力学变量为正则变换g_2:T*M→T*N。另一正则变换g_3:T*N→T*N给出全部热力学公式。Hamiltonian 正则方程给出诸热力学变量的时间演化。特别由dT/dt=-?H*/?S=0得到物质相变的条件之一为内压力P_I=0。可望通过研究材料的内压力寻找高临界温度超导体。

Let the dynamical canonical coordinates be a set of local coordinates ofthe 2n-dimensional symplectic manifold T*M, the thermodynamic variables (X,Y) and (S,T) be two sets of local coordinates on the submanifold T*N ofT*M, then from the dynamical variables to the thermodynamic variables is acanonical transformation g_2: T*M→T*N. Another canonical transformationg_3: T*N→T*N gives all of the thermodynamic formulas. The Hamilton's ca-nonical equations govern the time evolution of the thermodynamic variables.The equation dT/dt=-?H/?S=0 leads to the conclusion that one of the con-ditions of phase change is the internal pressure obeying P_t=(?U/?V)_T=0.