摘要
基于统计物理学中定义熵的一般公式,提出了单粒子坐标熵和动量熵的定义。从微观粒子的状态既可以用坐标表象中的波函数描述,也可以用动量表象中的波函数来描述出发,利用坐标几率密度函数ρ和动量几率密度函数w来定义粒子的坐标熵Sx和动量熵Sp,引用便于计算的谐振子基态来说明Sx与Sp之间的确存在着这种互补性,对线性振子其他态的计算,也证实了这种互补性的存在;推断出坐标熵与动量熵之间应该存在着一种互补关系:当粒子的微观状态发生变化时,若此过程使坐标熵增加,则其动量熵必减少;若此过程使坐标熵减少,则其动量熵必增加,论述了这两种熵之间存在互补性。并认为,这2种熵互补的根源来自不确定度关系,最后指出熵增长定律对坐标熵适用,而对动量熵不适用。
The difining equations of coordinate entropy and momentum entropy of single particle are proposed based on general formula for definition of entropy in statistical physics.The microscopic particle state can be used in the coordinate representation of the wave function description,and can also be used in the momentum representation of the wave function to describe the starting.Using the coordinates of the probability density function and the momentum probability density functions to define particle coordinates and momentum entropic,we use the calculated resonant oscillator in the ground state to illustrate the complementary existence.On the linear oscillator other state calculations also confirmed this complementarity existence.Infer the coordinates and momentum entropy,entropy should be complementary：when the particle microstructure changes,if in the process the coordinate entropy increase,its momentum entropy will reduce;if the process to coordinate entropy is reduced,then its momentum entropy will increase.The complementarity between these entropies which originates from uncertainty relation is demonstrated.Finally,it is pointed out that the principle of entropy increase is not suitable for momentum entropy.
出处
《沈阳师范大学学报（自然科学版）》
CAS
2012年第2期192-195,共4页
Journal of Shenyang Normal University:Natural Science Edition
基金
辽宁省教育厅高等教育教学改革研究重点项目(A-191)
关键词
坐标熵
动量熵
互补性
不确定度关系
coordinate entropy
momentum entropy
complementarity
uncertainty relation
