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粗略地说，耗散性理论对于线性系统的设计是有用的。耗散系统理论已经由V.M.Popov、J.C.Willems、D.J.Hill和P.Moylan讨论过。在线性不变系统的情况下，这被称为正实传递函数，一个基本的工具就是所谓的Kalman-Yakubovich-Popov引理，它联系了正实系统的状态空间和频域特性。

粗略地说，耗散性理论对于线性系统的设计是有用的。耗散系统理论已经由V.M.Popov、J.C.Willems、D.J.Hill和P.Moylan讨论过。在线性不变系统的情况下，这被称为正实传递函数，一个基本的工具就是所谓的Kalman-Yakubovich-Popov引理，它联系了正实系统的状态空间和频域特性。

== Quantum dissipative systems ==

== 量子耗散系统 Quantum dissipative systems ==

 

{{main|Quantum dissipation}}

{{main|Quantum dissipation}}

As quantum mechanics, and any classical dynamical system, relies heavily on Hamiltonian mechanics for which time is reversible, these approximations are not intrinsically able to describe dissipative systems. It has been proposed that in principle, one can couple weakly the system – say, an oscillator – to a bath, i.e., an assembly of many oscillators in thermal equilibrium with a broad band spectrum, and trace (average) over the bath. This yields a master equation which is a special case of a more general setting called the Lindblad equation that is the quantum equivalent of the classical Liouville equation. The well-known form of this equation and its quantum counterpart takes time as a reversible variable over which to integrate, but the very foundations of dissipative structures imposes an irreversible and constructive role for time.

As quantum mechanics, and any classical dynamical system, relies heavily on Hamiltonian mechanics for which time is reversible, these approximations are not intrinsically able to describe dissipative systems. It has been proposed that in principle, one can couple weakly the system – say, an oscillator – to a bath, i.e., an assembly of many oscillators in thermal equilibrium with a broad band spectrum, and trace (average) over the bath. This yields a master equation which is a special case of a more general setting called the Lindblad equation that is the quantum equivalent of the classical Liouville equation. The well-known form of this equation and its quantum counterpart takes time as a reversible variable over which to integrate, but the very foundations of dissipative structures imposes an irreversible and constructive role for time.

正如量子力学，和任何经典的动力系统，严重依赖于时间是可逆的哈密顿力学，这些近似本质上不能描述耗散系统。有人提出，原则上，一个人可以弱耦合系统---- 说，一个振荡器---- 浴，也就是说，许多振荡器组合在一个宽带光谱的热平衡，和迹(平均值)在浴。这就产生了一个主方程，这个主方程是一个被称为林德布劳德方程方程的更一般设置的特殊情况，它是经典 Liouville 方程的量子等价物。这个方程的众所周知的形式及其量子对应物需要时间作为可逆变量进行积分，但耗散结构的基础对时间起着不可逆和建设性的作用。

正如'''量子力学 Quantum Mechanics'''，和任何经典的'''动力系统 Dynamical System'''，严重依赖于时间是可逆的'''哈密顿力学 Hamiltonian mechanics'''，这些近似本质上不能描述耗散系统。有人提出，原则上，一个人可以弱耦合系统---- 说，一个振荡器---- 浴，也就是说，许多振荡器组合在一个宽带光谱的热平衡，和迹(平均值)在浴。这就产生了一个主方程，这个主方程是一个被称为林德布劳德方程方程的更一般设置的特殊情况，它是经典 Liouville 方程的量子等价物。这个方程的众所周知的形式及其量子对应物需要时间作为可逆变量进行积分，但耗散结构的基础对时间起着不可逆和建设性的作用。

 

 

 

 

==Applications on dissipative systems of dissipative structure concept==

==Applications on dissipative systems of dissipative structure concept==