The Principle of Minimal Resistance in Non-equilibrium Thermodynamics

详细信息    查看全文

• 作者：Roberto Mauri
• 关键词：Principle of minimal resistance ; Hamiltonian density time rate ; Non ; equilibrium thermodynamics ; Path integration
• 刊名：Foundations of Physics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：46
• 期：4
• 页码：393-408
• 全文大小：475 KB
• 参考文献：1.Kirchhoff, G.D.: Ueber die Anwendbarkeit der Formeln for die Intensitfiten der galvanischen Strome in einem Systeme linearer leiter auf Systemen, die zum Theil aus nicht linearem Leitern bestehen. Ann. Phys. 75, 189–205 (1848)CrossRef
  2.Prigogine, I.: Introduction to Thermodynamics of Irreversible Processes, 2nd edn. Interscience, New York (1961)MATH
  3.De Groot, S.R., Mazur, P.: Non-Equilibrium Thermodynamics. North Holland, Amsterdam (1962)
  4.Jaynes, E.T.: The minimum entropy production principle. Ann. Rev. Phys. Chem. 31, 579–601 (1980)CrossRef ADS
  5.Müller, I., Weiss, W.: Thermodynamics of irreversible processes - past and present. Eur. Phys. J. H 37, 139–236 (2012)CrossRef
  6.Ziegler, H.: An Introduction to Thermomechanics. North-Holland, Amsterdam (1983)MATH
  7.Hill, R.: The Mathematical Theory of Plasticity. Oxford University Press, Oxford (1950)MATH
  8.Onsager, L.: Reciprocal relations in irreversible processes II. Phys. Rev. 38, 2265–2279 (1931)CrossRef ADS MATH
  9.Onsager, L., Machlup, S.: Fluctuations and irreversible processes. Phys. Rev. 91, 1505–1512 (1953)CrossRef ADS MathSciNet MATH
  10.Gyarmati, I.: Non-Equilibrium Thermodynamics. Springer, Heidelberg (1970)CrossRef
  11.Zupanović, P., Yuretić, D., Botrić, S.: Kirchhoff’s loop law and the maximum entropy production principle. Phys. Rev. E 70, 056108 (2004)CrossRef ADS
  12.Martyushev, L.M., Seleznev, V.D.: Maximum entropy production principle in physics, chemistry and biology. Phys. Rep. 426, 1–45 (2006)CrossRef ADS MathSciNet
  13.Dewar, R.C.: Maximum entropy production and the fluctuation theorem. J. Phys. A 38, L371–L381 (2005)CrossRef ADS MathSciNet MATH
  14.Favretti, M.: The maximum entropy rate description of a thermodynamic system in a stationary non-equilibrium state. Entropy 11, 675–687 (2009)CrossRef ADS MathSciNet MATH
  15.Polettini, M.: Fact-checking Ziegler’s maximum entropy production principle beyond the linear regime and towards steady state. Entropy 15, 2570–2584 (2013)CrossRef ADS MathSciNet
  16.Martyushev, L.M.: Entropy and entropy production: old misconceptions and new breakthroughs. Entropy 15, 1152–1170 (2013)CrossRef ADS MathSciNet MATH
  17.Verhàs, J.: Gyarmati’s variational principle of dissipative processes. Entropy 16, 2362–2383 (2014)CrossRef ADS MathSciNet
  18.Salamon, P., Hoffmann, K.H., Schubert, S., Berry, R.S., Andresen, B.: What conditions make minimum entropy production equivalent to maximum power production? J. Non Equilib. Thermodyn. 26, 73–83 (2001)CrossRef ADS MATH
  19.Polettini, M.: Macroscopic constraints for the minimum entropy production principle. Phys. Rev. E 84(051117), 1–9 (2011)
  20.Beretta, G.P.: Modeling non-equilibrium dynamics of a discrete probability distribution: general rate equation for maximal entropy generation in a maximum-entropy landscape with time-dependent constraints. Entropy 10, 160–182 (2008)CrossRef ADS MathSciNet MATH
  21.Beretta, G.P.: Steepest entropy ascent model for far-nonequilibrium thermodynamics: unified implementation of the maximum entropy production principle. Phys. Rev. E 90, 1–14 (2014)CrossRef
  22.Uhlenbeck, G.E., Ornstein, L.S.: On the theory of the Brownian motion. Phys. Rev. 36, 823–841 (1930)CrossRef ADS MATH
  23.Mauri, R.: Non-Equilibrium Thermodynamics in Multiphase Flows. Springer, Heidelberg (2013)CrossRef MATH
  24.Mauri, R., Leporini, D.: Violation of the fluctuation-dissipation theorem in confined driven colloids. Europhys. Lett. 76, 1022–1028 (2006)CrossRef ADS
  25.Feynman, R.P., Hibbs, A.R.: Quantum Mechanics and Path Integrals. McGraw Hill, New York (1965)MATH
  26.Graham, R.: Path integral formulation of general diffusion processes. Z. Physik B 26, 281–290 (1977)CrossRef ADS
  27.Wang, Q.A., El Kaabouchiu, A.: From random motion of Hamiltonian systems to Boltzmann’s H theorem and second law of thermodynamics: a pathway by path probability. Entropy 16, 885–894 (2014)CrossRef ADS MathSciNet
  28.Gelfand, I.M., Yaglom, A.M.: Integration in function spaces and its application in quantum physics. J. Math. Phys. 1, 48–69 (1960)CrossRef ADS
  29.Schulman, L.S.: Techniques and Applications of Path Integration, Chapter 9. Interscience, New York (1981)
  30.Wiener, N.: The average of an analytic functional. Proc Nat. Acad. Sci. USA 7, 253–260; 294–298 (1921)
  31.Wieger, F.W.: Introduction to Path Integral Methods in Physics and Polymer Science. World Scientific, Singapore (1986)
  32.Martiouchev, L.M., Seleznev, V.D.: Maximum-entropy production principle as a criterion for the morphological-phase selection in the crystallization process. Dokl Phys 45, 129–131 (2000)CrossRef ADS
  33.Molin, D., Mauri, R.: Spinodal decomposition of binary mixtures with composition-dependent heat conductivities. Chem. Eng. Sci. 63, 2402–2407 (2008)CrossRef
  34.Mauri, R., Haber, S.: Applications of the Wiener path integral for the diffusion of Brownian particles in shear flows. SIAM J. Appl. Math. 46, 49–55 (1986)CrossRef MathSciNet MATH
  35.Foister, R.T., Van De Ven, T.G.M.: Diffusion of Brownian particles in shear flows. J. Fluid Mech. 96, 105–132 (1980)CrossRef ADS MATH
  36.Katayama, Y., Terauti, R.: Brownian motion of a single particle under shear flow. Eur. J. Phys. 17, 136–140 (1996)CrossRef
  
• 作者单位：Roberto Mauri (1)
  
  1. Department of Civil and Industrial Engineering, Laboratory of Reactive Multiphase Flows, Università di Pisa, 56126, Pisa, Italy
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Physics
  Quantum Physics
  Relativity and Cosmology
  Biophysics and Biomedical Physics
  Mechanics
  Condensed Matter
  
• 出版者：Springer Netherlands
• ISSN：1572-9516

文摘

Analytical models describing the motion of colloidal particles in given force fields are presented. In addition to local approaches, leading to well known master equations such as the Langevin and the Fokker–Planck equations, a global description based on path integration is reviewed. A new result is presented, showing that under very broad conditions, during its evolution a dissipative system tends to minimize its energy dissipation in such a way to keep constant the Hamiltonian time rate, equal to the difference between the flux-based and the force-based Rayleigh dissipation functions. In fact, the Fokker–Planck equation can be interpreted as the Hamilton–Jacobi equation resulting from such minumum principle. At steady state, the Hamiltonian time rate is maximized, leading to a minimum resistance principle. In the unsteady case, we consider the relaxation to equilibrium of harmonic oscillators and the motion of a Brownian particle in shear flow, obtaining results that coincide with the solution of the Fokker–Planck and the Langevin equations.