耦合振子的热力学临界性
Thermodynamic criticality of coupled oscillators
AI总结：
该研究针对有限尺寸同步振子系统，将平衡热力学标度关系拓展至非平衡同步动力学，验证了Rushbrooke不等式的适用性，确立了可系统应用的有限尺寸标度方法。
AI中文摘要：
诸如Rushbrooke不等式之类的严格热力学标度关系，从根本上是针对热力学极限下的平衡临界现象建立的。在呈现同步现象的有限尺寸动力学系统中，这类恒等式的直接应用会受到网络有限性以及自发同步相变的非平衡性质的双重阻碍。为规避这一难题，我们对具有非线性耦合的有限动力学振子系统中序参量、磁化率和比热的动力学对应量展开严谨研究，通过测量这些量随系统尺寸的变化，提取支配该相变的相关临界指数。我们通过直接验证Rushbrooke不等式来检验热力学映射的有效性，结果表明，标准平衡热力学标度架构可系统应用于非平衡同步动力学的有限尺寸标度。
英文摘要：
Strict thermodynamic scaling relations, such as the Rushbrooke inequality, are fundamentally established for equilibrium critical phenomena in the thermodynamic limit. In finite-size dynamical systems exhibiting synchronization, the direct application of such identities is hindered both by the finiteness of the network and the nonequilibrium nature of the spontaneous synchronization transition. To bypass this difficulty, we rigorously study the dynamical counterparts of the order parameter, susceptibility, and specific heat in finite systems of dynamical oscillators with nonlinear coupling. By measuring these quantities as a function of system size, we extract the associated critical exponents governing the transition. The validity of our thermodynamic mapping is tested by directly confirming the Rushbrooke inequality. Our results establish that standard equilibrium thermodynamic scaling architectures can be systematically applied to the finite-size scaling of nonequilibrium synchronization dynamics.
