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引用次数: 0
摘要
在这里,我们仔细研究了与广义吉布斯集合相关的随机过程的物理意义,并特别关注小系统的热力学波动。所谓的随机热力学是从热力学第一和第二定律的随机版本出发,将热力学量与微观变量联系在一起,与此不同,我们在这里直接考虑宏观变量中的随机变异性。通过认识吉布斯集合的势能结构(用势能熵生成函数表示),我们得到了宏观变量的精确非线性热力学朗格文方程(TLEs),其漂移用熵力表示。对理想单原子气体的典型集合和相关 TLEs 的分析表明,引入电流会导致非平衡传热条件,对熵的产生有有趣的限制,但没有明显的热力学极限。对于恒力作用下的胶体粒子,宏观变量的 TLE 与随机热力学通常使用的微观位置变量的 TLE 不同;TLE 与从哈密顿方程得到的基本方程一致,而随机热力学要求等温条件和熵与位置成正比。
The physical significance of the stochastic processes associated to the generalized Gibbs ensembles is scrutinized here with special attention to the thermodynamic fluctuations of small systems. Differently from the so-called stochastic thermodynamics, which starts from stochastic versions of the first and second law of thermodynamics and associates thermodynamic quantities to microscopic variables, here we consider stochastic variability directly in the macroscopic variables. By recognizing the potential structure of the Gibbs ensembles, when expressed as a function of the potential entropy generation, we obtain exact nonlinear thermodynamic Langevin equations (TLEs) for macroscopic variables, with drift expressed in terms of entropic forces. The analysis of the canonical ensemble for an ideal monoatomic gas and the related TLEs show that introducing currents leads to nonequilibrium heat transfer conditions with interesting bounds on entropy production but with no obvious thermodynamic limit. For a colloidal particle under constant force, the TLEs for macroscopic variables are different from those for the microscopic position, typically used in stochastic thermodynamics; while TLEs are consistent with the fundamental equation obtained from the Hamiltonian, stochastic thermodynamics requires isothermal conditions and entropy proportional to position.
期刊介绍:
Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.