By Roderick C. Dewar, Charles H. Lineweaver, Robert K. Niven, Klaus Regenauer-Lieb
The moment legislation, a cornerstone of thermodynamics, governs the common course of dissipative, non-equilibrium methods. however it says not anything approximately their real charges or the likelihood of fluctuations concerning the typical. This interdisciplinary e-book, written and peer-reviewed by means of foreign specialists, provides fresh advances within the look for new non-equilibrium ideas past the second one legislations, and their purposes to a variety of structures throughout physics, chemistry and biology. past the second one legislations brings jointly normally remoted components of non-equilibrium examine and highlights possibly fruitful connections among them, with entropy construction enjoying the unifying function. Key theoretical ideas contain the utmost Entropy creation precept, the Fluctuation Theorem, and the utmost Entropy approach to statistical inference. functions of those ideas are illustrated in such various fields as climatology, cosmology, crystal development morphology, Earth method technological know-how, environmental physics, evolutionary biology and expertise, fluid turbulence, microbial biogeochemistry, plasma physics, and radiative delivery, utilizing a large choice of analytical and experimental concepts. past the second one legislations will attract scholars and researchers wishing to achieve an figuring out of entropy creation and its vital position within the technology of non-equilibrium structures – either intimately and when it comes to the larger picture.
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Extra resources for Beyond the Second Law: Entropy Production and Non-equilibrium Systems
It compares the probability of observing an arbitrary system trajectory with the probability of observing the time reverse of that trajectory (its conjugate antitrajectory) in the same ensemble of trajectories : Xt ðCð0ÞÞ ¼ ln PðCð0Þ; 0Þ : PðCÃ ðtÞ; 0Þ ð2:2Þ 2 The Dissipation Function: Its Relationship to Entropy Production 33 Here C fq1 ; p1 ; . qN ; pN g is the phase space vector of the system which corresponds to a system trajectory, Xt ðCð0ÞÞ is the total dissipation (or time integral of the dissipation) for a trajectory originating at Cð0Þ and evolving for a time t, PðCð0Þ; 0Þ ¼ f ðCð0Þ; 0ÞdCð0Þ is the probability of observing a system in an infinitesimal region around Cð0Þ in the initial system distribution with distribution function f ðCð0Þ; 0Þ, and CÃ ðtÞ is the result of applying a time reversal map to CðtÞ.
Phys. Rev. E 64, 026303 (2001) 28. : Borders of disorders: in turbulent channel flow. J. Fluid Mech. 489, 185–198 (2003) 29. : A parametric sensitivity study of entropy production and kinetic energy dissipation using the FAMOUS AOGCM. Clim. Dyn. 38, 1211–1227 (2012) 30. : Über die Beziehung zwischen dem zweiten Hauptsatze der mechanischen Wärmetheorie und der Wahrscheinlichkeitsrechnung respektive den Sätzen über das Wärmegleichgewicht. Wien. Ber. 76, 373–435 (1877) 31. : Elementary principles of statistical mechanics.
13, 20] has yet to be given explicitly (cf. Chap. 12). Finally, can MaxEnt provide a theoretical basis for a non-stationary version of MaxEP? (road 14). A time-dependent formulation of MaxEP is explored by Vallino et al. (Chap. 18) in the context of biogeochemistry; see also [39, 50]. If such a principle could be established, entropy production might be to macroscopic dynamics what the Lagrangian functional is to microscopic dynamics (cf. Chap. 5, Sect. 5). 24 R. C. Dewar et al. 1. Its potential in this regard stems largely from its generic nature—in all problems the same principle is applied (maximum relative entropy); only the nature of the outcomes i and constraints C differs between problems.