更改

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。

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==

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

 

 

 

 

 

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>

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、族群动态、生长和化学机械结构

耗散结构框架作为一种理解系统在能量不断交换中行为的机制，已经成功地应用于不同的科学领域和应用，如光学、族群动态、生长和化学机械结构

== See also ==

== See also ==