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耗散系统 (查看源代码)

2020年8月11日 (二) 15:58的版本

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As [[quantum mechanics]], and any classical [[dynamical system]], relies heavily on [[Hamiltonian mechanics]] for which [[Time reversibility|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's theorem (Hamiltonian)|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 [[H-theorem|irreversible]] and constructive role for time.

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由于'''量子力学 Quantum Mechanics'''，以及所有经典的'''动力系统 Dynamical System'''都严重依赖于时间可逆的'''哈密顿力学 Hamiltonian mechanics'''，因此这些近似在本质上不能描述耗散系统。有人提出，原则上，人们可以将系统（例如，一个振荡器）弱耦合到'''浴bath'''中，'''i.e., an assembly of many oscillators in thermal equilibrium with a broad band spectrum, and trace (average) over the bath. 即在热平衡状态下具有宽带光谱的多个振荡器的组合，和浴上的迹(平均值)。'''这就产生了一个主方程，这是一个较为普遍的情况下的特例，被称为'''林德布劳德方程Lindblad equation'''，它是经典'''刘维尔方程Liouville equation'''的量子等价物。众所周知，这个方程和它的量子对应物把时间作为一个可逆变量来积分，但耗散结构的基础认为时间具有不可逆且建设性的作用。

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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.

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由于'''量子力学 Quantum Mechanics'''，以及所有经典的'''动力系统 Dynamical System'''都严重依赖于时间可逆的'''哈密顿力学 Hamiltonian mechanics'''，因此这些近似在本质上不能描述耗散系统。有人提出，原则上，人们可以将系统（例如，一个振荡器）弱耦合到'''浴bath'''中，'''即在热平衡状态下具有宽带光谱的多个振荡器的组合，和浴上的迹(平均值)。'''这就产生了一个主方程，这是一个较为普遍的情况下的特例，被称为'''林德布劳德方程Lindblad equation'''，它是经典'''刘维尔方程Liouville equation'''的量子等价物。众所周知，这个方程和它的量子对应物把时间作为一个可逆变量来积分，但耗散结构的基础认为时间具有不可逆且建设性的作用。

== 耗散结构概念在耗散系统中的应用 Applications on dissipative systems of dissipative structure concept ==

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