Stochastic kinematic description of a complex dynamics is shown to dictate an energetic and thermodynamic structure. An energy function ##IMG## [http://ej.iop.org/images/0295-5075/131/5/50002/epl20266ieqn1.gif] {$\varphi(\textbf{x})$} emerges as the limit of the generalized, nonequilibrium free energy of a Markovian dynamics with vanishing fluctuations. In terms of the ∇ φ and its orthogonal field ##IMG## [http://ej.iop.org/images/0295-5075/131/5/50002/epl20266ieqn2.gif] {${\boldsymbol{\gamma}}(\textbf{x})\perp\nabla\varphi$} , a general vector field ##IMG## [http://ej.iop.org/images/0295-5075/131/5/50002/epl20266ieqn3.gif] {$\textbf{b}(\textbf{x})$} can be decomposed into ##IMG## [http://ej.iop.org/images/0295-5075/131/5/50002/epl20266ieqn4.gif] {$-\textbf{D}(\textbf{x})\nabla\varphi+{\boldsymbol{\gamma}}$} , where ##IMG## {$\nabla\cdot(\omega(\textbf{x}){\boldsymbol{...}

中文翻译：

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复杂动力学涌现能量学的运动学基础

复杂动力学的随机运动学描述表明，它决定了能量和热力学结构。能量函数## IMG ## [http://ej.iop.org/images/0295-5075/131/5/50002/epl20266ieqn1.gif] {$ \ varphi（\ textbf {x}）$}随着出现具有消失的马尔可夫动力学的广义，非平衡自由能的极限。根据∇及其正交场## IMG ## [http://ej.iop.org/images/0295-5075/131/5/50002/epl20266ieqn2.gif] {$ {\ boldsymbol {\ gamma }}（\ textbf {x}）\ perp \ nabla \ varphi $}，通用向量字段## IMG ## [http://ej.iop.org/images/0295-5075/131/5/50002/ epl20266ieqn3.gif] {$ \ textbf {b}（\ textbf {x}）$}可以分解为## IMG ## [http://ej.iop.org/images/0295-5075/131/5/ 50002 / epl20266ieqn4.gif] {$-\ textbf {D}（\ textbf {x}）\ nabla \ varphi + {\ boldsymbol {\ gamma}} $}，