“耗散系统”的版本间的差异

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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。
 
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。
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== 参见==

2020年8月11日 (二) 16:05的版本

耗散系统 Dissipative system 是一种远离热力学平衡的热力学开放系统，运行在与之交换能量和物质的环境中。例如，龙卷风可以被认为是一个耗散系统。

耗散结构 Sissipative Structure是一种耗散系统，其 动力学性质dynamical régime在某种意义上是一种可重复的稳定状态。可以通过系统的自然进化、使用技巧来进化或两者的结合来达到这种可重复的稳定状态。

概览

耗散结构的特点是自发出现对称性破坏（各向异性）和形成复杂的、有时是混沌的结构，在这些结构中，相互作用的粒子展现出长程关联的性质。日常生活中的例子包括对流、湍流、旋风、飓风和生物体。较少见的例子包括激光、 b 细胞Bénard cells、液滴簇droplet cluster和BZ反应Belousov–Zhabotinsky reaction。


在关于游荡集合 Wandering Sets的文章中给出了一种对耗散系统进行数学建模的方法：这种方法涉及到一个可测集上的群的作用。


耗散系统也可以作为研究经济系统和复杂系统的工具。[1]例如，一个包含纳米线自组装的耗散系统被用作理解熵产生和生物系统鲁棒性之间关系的模型。[2]


热力学中的耗散结构

耗散结构一词是由俄罗斯-比利时的物理化学家伊利亚·普里高津 Ilya Prigogine发明的，他因在耗散结构方面的开创性工作获得了1977年的诺贝尔化学奖。普里高津Prigogine所考虑的耗散结构具有可被视为热力学稳态的动力学性质dynamical regimes，有时至少可以用合适的非平衡态热力学中的极值定理来描述。

在他的诺贝尔演讲中，[3]Prigogine解释了远离平衡的热力学系统如何与接近平衡的系统有着截然不同的行为。在平衡点附近，采用局部平衡假设，并可局部定义自由能和熵等典型热力学量。我们可以假定系统的（广义）通量和力之间是线性关系。线性热力学的两个著名成果是昂萨格倒易关系 Onsager reciprocal relations和最小熵产生定理 the principle of minimum entropy production。[4] 在努力将这些结果推广到远离平衡的系统之后，人们发现它们在这个系统中不成立，并且得到了相反的结果。


严格分析此类系统的一种方法是研究远离平衡的系统的稳定性。接近平衡点时，我们可以证明存在[[李亚普诺夫函数 Lyapunov function]]，它确保熵趋于稳定的最大值。波动在固定点附近被阻尼，宏观描述就已足够。然而，远离平衡的稳定性不再是一个普遍的性质，并且可以被打破。在化学系统中，这是在存在自催化反应的情况下发生的，例如在布鲁塞尔模型 Brusselator中。如果系统被驱动超过一定的阈值，振荡不再被阻尼，而是可能被放大。从数学上讲，这相当于一个霍普夫分岔 Hopf bifurcation，其中一个参数增加超过一定的值会导致极限环行为 limit cycle behavior。如果通过反应扩散方程来考虑空间效应，就会产生长程关联和空间有序模式spatially ordered patterns，[5]例如BZ反应 Belousov–Zhabotinsky reaction。由于不可逆过程而产生的具有这种物质动态状态的系统是耗散结构。


最近的研究重新考虑了Prigogine的耗散结构观点与生物系统的关系。[6]


控制论中的耗散系统

Willems首先在系统理论中引入耗散性的概念，[7]用输入输出特性来描述动力系统。考虑一个由其状态[math]\displaystyle{ x(t) }[/math]、输入[math]\displaystyle{ u(t) }[/math]和输出[math]\displaystyle{ y(t) }[/math]所描述的动力系统，输入-输出的相关性被给出了供给率[math]\displaystyle{ w(u(t),y(t)) }[/math]。如果存在一个连续可微的存储函数[math]\displaystyle{ V(x(t)) }[/math]，使得 [math]\displaystyle{ V(0)=0 }[/math], [math]\displaystyle{ V(x(t))\ge 0 }[/math]且[math]\displaystyle{ \dot{V}(x(t)) \le w(u(t),y(t)) }[/math].引用错误：没有找到与</ref>对应的<ref>标签


作为耗散性的一个特例，如果上述耗散性不等式对于被动供给率 [math]\displaystyle{ w(u(t),y(t)) = u(t)^Ty(t) }[/math]成立，则称系统为无源系统。


物理解释是，[math]\displaystyle{ V(x) }[/math]是储存在系统中的能量，而[math]\displaystyle{ w(u(t),y(t)) }[/math]是供给系统的能量。


这个概念与 李亚普诺夫稳定性 Lyapunov stability有很强的联系，其中，在动力系统能控性和可观测性一定的条件下，存储函数可以起到 李亚普诺夫函数Lyapunov functions的作用。


粗略地说，耗散理论对于设计线性和非线性系统的反馈控制律是有用的。V.M.Popov、J.C.Willems、D.J.Hill和P.Moylan讨论过耗散系统理论。在线性不变系统中，这被称为 正实传递函数positive real transfer functions，一个基本的工具就是所谓的Kalman-Yakubovich-Popov引理 Kalman–Yakubovich–Popov lemma，它关系到正实系统的状态空间和频域特性。[8]由于其重要的应用，耗散系统一直是系统与控制领域的研究热点。

量子耗散系统 Quantum dissipative systems

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。


耗散结构概念在耗散系统中的应用

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、族群动态population dynamics[9][10]、生长[11] [12][13]和化学机械结构[14][15][16]等。


参见

参考文献

  1. ↑ Chen, Jing (2015). The Unity of Science and Economics: A New Foundation of Economic Theory. https://www.springer.com/us/book/9781493934645: Springer. 
  2. ↑ Hubler, Alfred; Belkin, Andrey; Bezryadin, Alexey (2 January 2015). "Noise induced phase transition between maximum entropy production structures and minimum entropy production structures?". Complexity. 20 (3): 8–11. Bibcode:2015Cmplx..20c...8H. doi:10.1002/cplx.21639.
  3. ↑ Prigogine, Ilya. "Time, Structure and Fluctuations". Nobelprize.org. PMID 17738519.
  4. ↑ Prigogine, Ilya (1945). "Modération et transformations irréversibles des systèmes ouverts". Bulletin de la Classe des Sciences, Académie Royale de Belgique. 31: 600–606.
  5. ↑ Lemarchand, H.; Nicolis, G. (1976). "Long range correlations and the onset of chemical instabilities". Physica. 82A (4): 521–542. Bibcode:1976PhyA...82..521L. doi:10.1016/0378-4371(76)90079-0.
  6. ↑ England, Jeremy L. (4 November 2015). "Dissipative adaptation in driven self-assembly". Nature Nanotechnology. 10 (11): 919–923. Bibcode:2015NatNa..10..919E. doi:10.1038/NNANO.2015.250. PMID 26530021.
  7. ↑ Willems, J.C. (1972). "Dissipative dynamical systems part 1: General theory" (PDF). Arch. Rational Mech. Anal. 45 (5): 321. Bibcode:1972ArRMA..45..321W. doi:10.1007/BF00276493. hdl:10338.dmlcz/135639.
  8. ↑ Bao, Jie; Lee, Peter L. (2007). Process Control - The Passive Systems Approach. Springer Business+Science Media. doi:10.1007/978-1-84628-893-7. ISBN 978-1-84628-892-0. https://www.springer.com/978-1-84628-892-0. 
  9. ↑ Lugiato, L. A.; Prati, F.; Gorodetsky, M. L.; Kippenberg, T. J. (28 December 2018). "From the Lugiato–Lefever equation to microresonator-based soliton Kerr frequency combs". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 376 (2135): 20180113. arXiv:1811.10685. Bibcode:2018RSPTA.37680113L. doi:10.1098/rsta.2018.0113. PMID 30420551.
  10. ↑ Andrade-Silva, I.; Bortolozzo, U.; Castillo-Pinto, C.; Clerc, M. G.; González-Cortés, G.; Residori, S.; Wilson, M. (28 December 2018). "Dissipative structures induced by photoisomerization in a dye-doped nematic liquid crystal layer". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 376 (2135): 20170382. Bibcode:2018RSPTA.37670382A. doi:10.1098/rsta.2017.0382. PMC 6232603. PMID 30420545.
  11. ↑ Zykov, V. S. (28 December 2018). "Spiral wave initiation in excitable media". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 376 (2135): 20170379. Bibcode:2018RSPTA.37670379Z. doi:10.1098/rsta.2017.0379. PMID 30420544.
  12. ↑ Tlidi, M.; Clerc, M. G.; Escaff, D.; Couteron, P.; Messaoudi, M.; Khaffou, M.; Makhoute, A. (28 December 2018). "Observation and modelling of vegetation spirals and arcs in isotropic environmental conditions: dissipative structures in arid landscapes". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 376 (2135): 20180026. Bibcode:2018RSPTA.37680026T. doi:10.1098/rsta.2018.0026. PMID 30420548.
  13. ↑ Gunji, Yukio-Pegio; Murakami, Hisashi; Tomaru, Takenori; Basios, Vasileios (28 December 2018). "Inverse Bayesian inference in swarming behaviour of soldier crabs". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 376 (2135): 20170370. Bibcode:2018RSPTA.37670370G. doi:10.1098/rsta.2017.0370. PMC 6232598. PMID 30420541.
  14. ↑ Bullara, D.; De Decker, Y.; Epstein, I. R. (28 December 2018). "On the possibility of spontaneous chemomechanical oscillations in adsorptive porous media". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 376 (2135): 20170374. Bibcode:2018RSPTA.37670374B. doi:10.1098/rsta.2017.0374. PMC 6232597. PMID 30420542.
  15. ↑ Gandhi, Punit; Zelnik, Yuval R.; Knobloch, Edgar (28 December 2018). "Spatially localized structures in the Gray–Scott model". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 376 (2135): 20170375. Bibcode:2018RSPTA.37670375G. doi:10.1098/rsta.2017.0375. PMID 30420543.
  16. ↑ Kostet, B.; Tlidi, M.; Tabbert, F.; Frohoff-Hülsmann, T.; Gurevich, S. V.; Averlant, E.; Rojas, R.; Sonnino, G.; Panajotov, K. (28 December 2018). "Stationary localized structures and the effect of the delayed feedback in the Brusselator model". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 376 (2135): 20170385. arXiv:1810.05072. Bibcode:2018RSPTA.37670385K. doi:10.1098/rsta.2017.0385. PMID 30420547.

其他资料

  • B. Brogliato, R. Lozano, B. Maschke, O. Egeland, Dissipative Systems Analysis and Control. Theory and Applications. Springer Verlag, London, 2nd Ed., 2007.
  • Philipson, Schuster, Modeling by Nonlinear Differential Equations: Dissipative and Conservative Processes, World Scientific Publishing Company 2009.
  • J.C. Willems. Dissipative dynamical systems, part I: General theory; part II: Linear systems with quadratic supply rates. Archive for Rationale mechanics Analysis, vol.45, pp. 321–393, 1972.

相关链接 External links

Category:Thermodynamic systems

类别: 热力学系统

Category:Systems theory

范畴: 系统论

Category:Non-equilibrium thermodynamics

类别: 非平衡态热力学


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