Lima Henrique Santos, Tsallis Constantino, Nobre Fernando Dantas
Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, RJ, Brazil.
National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, RJ, Brazil.
Entropy (Basel). 2023 Dec 25;26(1):0. doi: 10.3390/e26010025.
The thermal conductance of a one-dimensional classical inertial Heisenberg model of linear size is computed, considering the first and last particles in thermal contact with heat baths at higher and lower temperatures, Th and Tl (Th>Tl), respectively. These particles at the extremities of the chain are subjected to standard Langevin dynamics, whereas all remaining rotators (i=2,⋯,L-1) interact by means of nearest-neighbor ferromagnetic couplings and evolve in time following their own equations of motion, being investigated numerically through molecular-dynamics numerical simulations. Fourier's law for the heat flux is verified numerically, with the thermal conductivity becoming independent of the lattice size in the limit L→∞, scaling with the temperature, as κ(T)∼T-2.25, where T=(Th+Tl)/2. Moreover, the thermal conductance, σ(L,T)≡κ(T)/L, is well-fitted by a function, which is typical of nonextensive statistical mechanics, according to σ(L,T)=Aexpq(-Bxη), where and are constants, x=L0.475T, q=2.28±0.04, and η=2.88±0.04.
计算了线性尺寸为 的一维经典惯性海森堡模型的热导率，其中考虑了链的第一个和最后一个粒子分别与温度较高和较低的热浴（(T_h)和(T_l)，(T_h>T_l)）热接触。链两端的这些粒子服从标准朗之万动力学，而所有其余的转子（(i = 2,\cdots,L - 1)）通过最近邻铁磁耦合相互作用，并根据它们自己的运动方程随时间演化，通过分子动力学数值模拟进行数值研究。通过数值验证了热流的傅里叶定律，在(L→∞)的极限情况下，热导率与晶格尺寸无关，随温度缩放，即(\kappa(T)∼T^{-2.25})，其中(T=(T_h + T_l)/2)。此外，热导(\sigma(L,T)≡\kappa(T)/L)很好地拟合为一个函数，这是典型的非广延统计力学函数，即(\sigma(L,T)=A\exp_q(-Bx^\eta))，其中(A)和(B)是常数，(x = L^{0.475}T)，(q = 2.28±0.04)，(\eta = 2.88±0.04)。
