Meibohm Jan, Esposito Massimiliano
<a href="https://ror.org/03v4gjf40">Technische Universität Berlin</a>, Straße des 17. Juni 135, 10623 Berlin, Germany.
Department of Mathematics, <a href="https://ror.org/0220mzb33">King's College London</a>, London WC2R 2LS, United Kingdom.
Phys Rev E. 2024 Oct;110(4-1):044114. doi: 10.1103/PhysRevE.110.044114.
We study driven q-state Potts models with thermodynamically consistent dynamics and global coupling. For a wide range of parameters, these models exhibit a dynamical phase transition from decoherent oscillations into a synchronized phase. Starting from a general microscopic dynamics for individual oscillators, we derive the normal form of the high-dimensional Hopf bifurcation that underlies the phase transition. The normal-form equations are exact in the thermodynamic limit and close to the bifurcation. Exploiting the symmetry of the model, we solve these equations and thus uncover the intricate stable synchronization patterns of driven Potts models, characterized by a rich phase diagram. Making use of thermodynamic consistency, we show that synchronization reduces dissipation in such a way that the most stable synchronized states dissipate the least entropy. Close to the phase transition, our findings condense into a linear dissipation-stability relation that connects entropy production with phase-space contraction, a stability measure. At finite system size, our findings suggest a minimum-dissipation principle for driven Potts models that holds arbitrarily far from equilibrium.
我们研究具有热力学一致动力学和全局耦合的驱动q态Potts模型。对于广泛的参数范围，这些模型表现出从退相干振荡到同步相的动力学相变。从单个振子的一般微观动力学出发，我们推导了作为相变基础的高维霍普夫分岔的范式。范式方程在热力学极限下是精确的，并且接近分岔点。利用模型的对称性，我们求解这些方程，从而揭示驱动Potts模型复杂的稳定同步模式，其特征是具有丰富的相图。利用热力学一致性，我们表明同步以这样一种方式减少耗散，即最稳定的同步状态耗散的熵最少。接近相变时，我们的发现凝聚成一个线性耗散 - 稳定性关系，该关系将熵产生与相空间收缩（一种稳定性度量）联系起来。在有限系统规模下，我们的发现表明驱动Potts模型存在一个远离平衡任意远都成立的最小耗散原理。
