The Spatial Distribution Of Thermal Energy Of The Coupled Spring System

The thermodynamic properties of many body systems in statistical physics have been an important issue.Under the condition of thermodynamic equilibrium,the uncoupled system satisfies the equipartition theorem.Recently,the thermal properties of coupling system is an important research direction.The degrees of freedom can be decoupled through orthogonal transformation.However,the factors affecting the spatial distribution of thermal energy is not clear yet,so the influence of four factors on spatial distribution of thermal energy on some two-dimensional triangular lattice models is studied,they are: the boundary conditions,the number of degrees of freedom and springs,the neighbors of springs and the geometric structure of the model.The main contents are as follows:1.The spatial distribution of thermal energy in the triangle chains model with two chains under different boundary conditions is studied.The influence of the boundary conditions,the number of springs and degrees of freedom,and the geometric structure of the model on the spatial distribution of thermal energy is discussed.For this model which the number of springs is not much greater than the number of degrees of freedom,the influence of boundary conditions on spatial distribution exited only when the model is small.When the model is large,the spatial distribution of thermal energy is always homogeneous,so the influence of boundary conditions is local and finite.When the geometric structure of the triangle chains model changes,the spatial distribution of thermal energy is always inhomogeneous and invariable.The result indicate that the spatial distribution of thermal energy distribution is not affected by the geometric structure of this model.2.For the complex two-dimensional triangular lattice with three chains and eight chains(the number of spring is much greater than degrees of freedom),it is studied that the influence of boundary conditions,neighbors of springs and the geometric structure of the model on the spatial distribution of thermal energy.The spatial distribution of thermal energy is affected by the neighbors of springs and the geometric structure of the model.It is found that the spatial distribution of thermal energy may be inhomogeneous only when the number of springs is much greater than degrees of freedom.That is,it will produce the inhomogeneous spatial distribution of thermal energy when the coupling interaction of system is strong.The less the neighbors of springs is,the higher the average thermal energy is.In order to investigate the influence of the asymmetric model on spatial distribution of thermal energy,some springs have few neighbors on the two-dimensional triangular lattice with eight chains,and the average thermal energy of these springs is different with others.This shows that the more asymmetric the geometrical structure is,the more inhomogeneous the spatial distribution of thermal energy is.The geometric structure of the model can change the spatial distribution of thermal energy,which can be applied in the field to research the thermal properties of proteins.