Komatsu Nobuyoshi, Kimura Shigeo, Kiwata Takahiro
Department of Mechanical Systems Engineering, Kanazawa University, Kanazawa, Ishikawa 920-1192, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 1):041107. doi: 10.1103/PhysRevE.80.041107. Epub 2009 Oct 6.
Gravity-dominated systems have a negative specific heat. We investigate the negative specific heat of self-gravitating systems enclosed in a spherical container with reflecting walls by means of N-body simulations. To simulate nonequilibrium processes, a particle reflected at a nonadiabatic wall is cooled to mimic energy loss by reflecting walls, while an adiabatic wall is employed for microcanonical ensembles. We show that a negative specific heat occurs not only in the microcanonical ensemble but also in certain nonequilibrium processes with the nonadiabatic wall. With increasing cooling rates, the dependence of temperature T on energy epsilon , i.e., the epsilon-T curve, gradually deviates from the microcanonical ensemble and approaches a certain common curve at a low-energy region. The common curve agrees with an epsilon-T curve for stellar polytropes, especially for the polytrope index of n approximately 5 . We show that the stellar polytrope should be related to the present nonequilibrium process appearing in the self-gravitating system with the nonadiabatic wall. In the nonequilibrium process, a rapid change in velocity at the nonadiabatic wall significantly affects the velocity and density profiles. In particular, the greater the cooling rate, the greater the local velocity gradient at a low-energy region.
引力主导的系统具有负比热容。我们通过N体模拟研究了封闭在具有反射壁的球形容器中的自引力系统的负比热容。为了模拟非平衡过程，在非绝热壁处反射的粒子被冷却，以模拟反射壁造成的能量损失，而绝热壁则用于微正则系综。我们表明，负比热容不仅出现在微正则系综中，也出现在某些具有非绝热壁的非平衡过程中。随着冷却速率的增加，温度T对能量ε的依赖关系，即ε-T曲线，逐渐偏离微正则系综，并在低能量区域趋近于某一共同曲线。该共同曲线与恒星多方球的ε-T曲线一致，特别是对于多方指数n约为5的情况。我们表明，恒星多方球应该与具有非绝热壁的自引力系统中出现的当前非平衡过程有关。在非平衡过程中，非绝热壁处速度的快速变化会显著影响速度和密度分布。特别是，冷却速率越大，低能量区域的局部速度梯度就越大。
