http://prob140.org/textbook/content/Chapter_11/01_Balance_and_Detailed_Balance.html WebThe detailed balance equations are easy to solve sequentially: and so on, so that for 1 ≤ k ≤ N 1 ≤ k ≤ N , π(k) = (N k)π(0) π ( k) = ( N k) π ( 0) by a far easier induction than the one needed to solve the balance equations. The sum of the terms in the solution is. by the binomial theorem.

Metropolis Hastings algorithm Independent and Random-Walk

Two conditions are sufficient and necessary for solvability of the system of detailed balance equations: If k r + > 0 {\displaystyle k_ {r}^ {+}>0} then k r − > 0 {\displaystyle k_ {r}^ {-}>0} and, conversely, if k r − > 0... For any solution λ = ( λ r ) {\displaystyle {\boldsymbol {\lambda }}= ... See more 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 … See more A Markov process is called a reversible Markov process or reversible Markov chain if it satisfies the detailed balance equations. These equations require that the See more For many systems of physical and chemical kinetics, detailed balance provides sufficient conditions for the strict increase of entropy in isolated systems. For example, the famous Boltzmann H-theorem states that, according to the Boltzmann … See more To describe dynamics of the systems that obey the generalized mass action law, one has to represent the activities as functions of the See more 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 … See more The microscopic "reversing of time" turns at the kinetic level into the "reversing of arrows": the elementary processes transform into their reverse processes. For example, the reaction transforms into and conversely. (Here, are … See more In chemical kinetics, the elementary reactions are represented by the stoichiometric equations where are the components and The See more WebDetailed balance is a very important concept in physics and chemistry. If a system satisfies detailed balance, then it is called an equilibrium system, or sometimes reversible in … raymond coil

Detailed balance - Wikiwand

WebThe principle of detailed balance can be used in kinetic systems which are decomposed into elementary processes . It states that at equilibrium, each elementary process is in equilibrium with its reverse process. ... Wegscheider's conditions for the generalized mass action law Dissipation in systems with detailed balance Onsager reciprocal ... WebDetailed balance. The crucial step is to prove that the so-called detailed balance condition holds (see Markov chains), which implies that the target distribution is the … WebA sufficient but not necessary condition is detailed balance, which requires that each transition ′ is reversible: for every pair of states , ′, the probability of being in state and … raymond coia