更改

由于'''<font color="#ff8000">量子力学 Quantum Mechanics</font>'''，以及所有经典的'''<font color="#ff8000">动力系统 Dynamical System</font>'''都严重依赖于时间可逆的'''<font color="#ff8000">哈密顿力学 Hamiltonian mechanics</font>'''，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'''<font color="#ff8000">浴bath</font>'''中，'''<font color="#32CD32">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)。</font>'''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'''<font color="#ff8000">林德布劳德方程Lindblad equation</font>'''，它是经典'''<font color="#ff8000">刘维尔方程Liouville equation</font>'''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。

由于'''<font color="#ff8000">量子力学 Quantum Mechanics</font>'''，以及所有经典的'''<font color="#ff8000">动力系统 Dynamical System</font>'''都严重依赖于时间可逆的'''<font color="#ff8000">哈密顿力学 Hamiltonian mechanics</font>'''，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'''<font color="#ff8000">浴bath</font>'''中，'''<font color="#32CD32">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)。</font>'''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'''<font color="#ff8000">林德布劳德方程Lindblad equation</font>'''，它是经典'''<font color="#ff8000">刘维尔方程Liouville equation</font>'''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 ==

== 耗散结构概念在耗散系统中的应用==

The framework of dissipative structures as a mechanism to understand the behavior of systems in constant interexchange of energy has been successfully applied on different science fields and applications, as in optics<ref>{{cite journal |last1=Lugiato |first1=L. A. |last2=Prati |first2=F. |last3=Gorodetsky |first3=M. L. |last4=Kippenberg |first4=T. J. |title=From the Lugiato–Lefever equation to microresonator-based soliton Kerr frequency combs |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |date=28 December 2018 |volume=376 |issue=2135 |pages=20180113 |doi=10.1098/rsta.2018.0113|pmid=30420551 |arxiv=1811.10685 |bibcode=2018RSPTA.37680113L }}</ref><ref>{{cite journal |last1=Andrade-Silva |first1=I. |last2=Bortolozzo |first2=U. |last3=Castillo-Pinto |first3=C. |last4=Clerc |first4=M. G. |last5=González-Cortés |first5=G. |last6=Residori |first6=S. |last7=Wilson |first7=M. |title=Dissipative structures induced by photoisomerization in a dye-doped nematic liquid crystal layer |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |date=28 December 2018 |volume=376 |issue=2135 |pages=20170382 |doi=10.1098/rsta.2017.0382|pmid=30420545 |pmc=6232603 |bibcode=2018RSPTA.37670382A }}</ref>, population dynamics and growth <ref>{{cite journal |last1=Zykov |first1=V. S. |title=Spiral wave initiation in excitable media |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |date=28 December 2018 |volume=376 |issue=2135 |pages=20170379 |doi=10.1098/rsta.2017.0379|pmid=30420544 |bibcode=2018RSPTA.37670379Z }}</ref> <ref>{{cite journal |last1=Tlidi |first1=M. |last2=Clerc |first2=M. G. |last3=Escaff |first3=D. |last4=Couteron |first4=P. |last5=Messaoudi |first5=M. |last6=Khaffou |first6=M. |last7=Makhoute |first7=A. |title=Observation and modelling of vegetation spirals and arcs in isotropic environmental conditions: dissipative structures in arid landscapes |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |date=28 December 2018 |volume=376 |issue=2135 |pages=20180026 |doi=10.1098/rsta.2018.0026|pmid=30420548 |bibcode=2018RSPTA.37680026T }}</ref><ref>{{cite journal |last1=Gunji |first1=Yukio-Pegio |last2=Murakami |first2=Hisashi |last3=Tomaru |first3=Takenori |last4=Basios |first4=Vasileios |title=Inverse Bayesian inference in swarming behaviour of soldier crabs |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |date=28 December 2018 |volume=376 |issue=2135 |pages=20170370 |doi=10.1098/rsta.2017.0370|pmid=30420541 |pmc=6232598 |bibcode=2018RSPTA.37670370G }}</ref> and chemomechanical structures<ref>{{cite journal |last1=Bullara |first1=D. |last2=De Decker |first2=Y. |last3=Epstein |first3=I. R. |title=On the possibility of spontaneous chemomechanical oscillations in adsorptive porous media |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |date=28 December 2018 |volume=376 |issue=2135 |pages=20170374 |doi=10.1098/rsta.2017.0374|pmid=30420542 |pmc=6232597 |bibcode=2018RSPTA.37670374B }}</ref><ref>{{cite journal |last1=Gandhi |first1=Punit |last2=Zelnik |first2=Yuval R. |last3=Knobloch |first3=Edgar |title=Spatially localized structures in the Gray–Scott model |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |date=28 December 2018 |volume=376 |issue=2135 |pages=20170375 |doi=10.1098/rsta.2017.0375|pmid=30420543 |bibcode=2018RSPTA.37670375G }}</ref><ref>{{cite journal |last1=Kostet |first1=B. |last2=Tlidi |first2=M. |last3=Tabbert |first3=F. |last4=Frohoff-Hülsmann |first4=T. |last5=Gurevich |first5=S. V. |last6=Averlant |first6=E. |last7=Rojas |first7=R. |last8=Sonnino |first8=G. |last9=Panajotov |first9=K. |title=Stationary localized structures and the effect of the delayed feedback in the Brusselator model |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |date=28 December 2018 |volume=376 |issue=2135 |pages=20170385 |doi=10.1098/rsta.2017.0385|pmid=30420547 |arxiv=1810.05072 |bibcode=2018RSPTA.37670385K }}</ref>

耗散结构框架作为一种理解系统在能量不断交换中的行为的机制，已经成功地应用于不同的科学领域和应用，如光学、'''<font color="#ff8000">族群动态population dynamics</font>'''<ref>{{cite journal |last1=Lugiato |first1=L. A. |last2=Prati |first2=F. |last3=Gorodetsky |first3=M. L. |last4=Kippenberg |first4=T. J. |title=From the Lugiato–Lefever equation to microresonator-based soliton Kerr frequency combs |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |date=28 December 2018 |volume=376 |issue=2135 |pages=20180113 |doi=10.1098/rsta.2018.0113|pmid=30420551 |arxiv=1811.10685 |bibcode=2018RSPTA.37680113L }}</ref><ref>{{cite journal |last1=Andrade-Silva |first1=I. |last2=Bortolozzo |first2=U. |last3=Castillo-Pinto |first3=C. |last4=Clerc |first4=M. G. |last5=González-Cortés |first5=G. |last6=Residori |first6=S. |last7=Wilson |first7=M. |title=Dissipative structures induced by photoisomerization in a dye-doped nematic liquid crystal layer |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |date=28 December 2018 |volume=376 |issue=2135 |pages=20170382 |doi=10.1098/rsta.2017.0382|pmid=30420545 |pmc=6232603 |bibcode=2018RSPTA.37670382A }}</ref>、生长<ref>{{cite journal |last1=Zykov |first1=V. S. |title=Spiral wave initiation in excitable media |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |date=28 December 2018 |volume=376 |issue=2135 |pages=20170379 |doi=10.1098/rsta.2017.0379|pmid=30420544 |bibcode=2018RSPTA.37670379Z }}</ref> <ref>{{cite journal |last1=Tlidi |first1=M. |last2=Clerc |first2=M. G. |last3=Escaff |first3=D. |last4=Couteron |first4=P. |last5=Messaoudi |first5=M. |last6=Khaffou |first6=M. |last7=Makhoute |first7=A. |title=Observation and modelling of vegetation spirals and arcs in isotropic environmental conditions: dissipative structures in arid landscapes |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |date=28 December 2018 |volume=376 |issue=2135 |pages=20180026 |doi=10.1098/rsta.2018.0026|pmid=30420548 |bibcode=2018RSPTA.37680026T }}</ref><ref>{{cite journal |last1=Gunji |first1=Yukio-Pegio |last2=Murakami |first2=Hisashi |last3=Tomaru |first3=Takenori |last4=Basios |first4=Vasileios |title=Inverse Bayesian inference in swarming behaviour of soldier crabs |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |date=28 December 2018 |volume=376 |issue=2135 |pages=20170370 |doi=10.1098/rsta.2017.0370|pmid=30420541 |pmc=6232598 |bibcode=2018RSPTA.37670370G }}</ref>和化学机械结构<ref>{{cite journal |last1=Bullara |first1=D. |last2=De Decker |first2=Y. |last3=Epstein |first3=I. R. |title=On the possibility of spontaneous chemomechanical oscillations in adsorptive porous media |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |date=28 December 2018 |volume=376 |issue=2135 |pages=20170374 |doi=10.1098/rsta.2017.0374|pmid=30420542 |pmc=6232597 |bibcode=2018RSPTA.37670374B }}</ref><ref>{{cite journal |last1=Gandhi |first1=Punit |last2=Zelnik |first2=Yuval R. |last3=Knobloch |first3=Edgar |title=Spatially localized structures in the Gray–Scott model |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |date=28 December 2018 |volume=376 |issue=2135 |pages=20170375 |doi=10.1098/rsta.2017.0375|pmid=30420543 |bibcode=2018RSPTA.37670375G }}</ref><ref>{{cite journal |last1=Kostet |first1=B. |last2=Tlidi |first2=M. |last3=Tabbert |first3=F. |last4=Frohoff-Hülsmann |first4=T. |last5=Gurevich |first5=S. V. |last6=Averlant |first6=E. |last7=Rojas |first7=R. |last8=Sonnino |first8=G. |last9=Panajotov |first9=K. |title=Stationary localized structures and the effect of the delayed feedback in the Brusselator model |journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |date=28 December 2018 |volume=376 |issue=2135 |pages=20170385 |doi=10.1098/rsta.2017.0385|pmid=30420547 |arxiv=1810.05072 |bibcode=2018RSPTA.37670385K }}</ref>等。

 

 

== 参见 See also ==

== 参见 See also ==