Detailed balance

The principle of detailed balance can be used in kinetic systems which are decomposed into elementary processes (collisions, or steps, or elementary reactions). It states that at equilibrium, each elementary process is in equilibrium with its reverse process. History The principle of detailed balance was explicitly introduced for collisions by Ludwig Boltzmann. In 1872, he proved his H-theorem using this principle. The arguments in favor of this property are founded upon microscopic reversibility. Five years before Boltzmann, James Clerk Maxwell used the principle of detailed balance for gas kinetics with the reference to the principle of sufficient reason. He compared the idea of detailed balance with other types of balancing (like cyclic balance) and found that "Now it is impossible to assign a reason" why detailed balance should be rejected (pg. 64). Albert Einstein in 1916 used the principle of detailed balance in a background for his quantum theory of emission and abs

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Formulation reproducing the ignition delays simulated by a detailed mechanism: Application to n-heptane combustion

This article is part of the project to model the kinetics of high-temperature combustions, occurring behind shock waves and in detonation waves. The "conventional" semi-empirical correlations of ignition delays have been reformulated, by keeping the Arrhenius equation form. It is shown how it polynomial with 3(N) Coefficients (where N is an element of [1, 4] is the number of adjustable kinetic parameters, likely to be simultaneously chosen among the temperature T, the pressure P, the inert fraction X-Ar, and the equivalence ratio Phi) can reproduce the delays predicted by the Curran et al. [H.J. Curran, P. Gaffuri, W.J. Pitz. C.K. Westbrook, Combust. Flame 129 (2002) 253-280] detailed mechanism (565 species and 22538 reactions), over it wide range of conditions (comparable with the validity domain). The deviations between the simulated times and their fits (typically 1%) are definitely lower than the Uncertainties related to the mechanism (at least 25%). In addition. using, this new formalism to evaluate these durations is about 10(6) times faster than simulating them With SENKIN (CHEMKIN III package) and only 10 times slower than using the classical correlations. The adaptation of the traditional method for predicting delays is interesting, for modeling. because those performances are difficult to obtain simultaneously with Other reduction methods (either purely mathematical, chemical, or even mixed). After a physical and mathematical justification of the proposed formalism, some of its potentialities for n-heptane combustion are presented. In particular, the trends of simulated delays and activation energies are shown for T is an element of [1500 K, 1900 K], P is an element of [10 kPa, 1 MPa] X-Ar is an element of [0, 0, 7], and Phi is an element of [0.25, 4.0]. (C) 2008 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

2008

Mechanistic study of the radical SAM-dependent amine dehydrogenation reactions

Xinjian Ji, Yue Yin, Shuguang Yuan, Qixing Zhang

The radical SAM enzyme NosL catalyzes the conversion of L-Trp to 3-methyl-2-indolic acid, and this reaction is initiated by the 5'-deoxyadenosyl (dAdo) radical-mediated hydrogen abstraction from the L-Trp amino group. We demonstrate here that when D-Trp was used in the NosL reaction, hydrogen abstraction occurs promiscuously at both the amino group and C alpha of D-Trp. These results inspired us to establish the detailed mechanism of L-Trp amine dehydrogenation catalyzed by a NosL mutant, and to engineer a novel radical SAM-dependent L-Tyr amine dehydrogenase from the thiamine biosynthesis enzyme ThiH.

Royal Soc Chemistry2016

Fluctuation-dissipation relations in the absence of detailed balance: formalism and applications to active matter

Sara Dal Cengio, Ignacio Pagonabarraga Mora

We present a comprehensive study about the relationship between the way detailed balance is broken in non-equilibrium systems and the resulting violations of the fluctuation-dissipation theorem. Starting from stochastic dynamics with both odd and even variables under time-reversal, we derive an explicit expression for the time-reversal operator, i.e. the Markovian operator which generates the time-reversed trajectories. We then exploit the relation between entropy production and the breakdown of detailed balance to establish general constraints on the non-equilibrium steady-states (NESS), which relate the non-equilibrium character of the dynamics with symmetry properties of the NESS distribution. This provides a direct route to derive extended fluctuation-dissipation relations, expressing the linear response function in terms of NESS correlations. Such framework provides a unified way to understand the departure from equilibrium of active systems and its linear response. We then consider two paradigmatic models of interacting self-propelled particles, namely active Brownian particles and active Ornstein-Uhlenbeck particles. We analyze the non-equilibrium character of these systems (also within a Markov and a Chapman-Enskog approximation) and derive extended fluctuation-dissipation relations for them, clarifying which features of these active model systems are genuinely non-equilibrium.

IOP PUBLISHING LTD2021

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