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A Markov process is called a reversible Markov process or reversible Markov chain if there exists a positive stationary distribution π that satisfies the detailed balance equations [13] =, where P ij is the Markov transition probability from state i to state j, i.e. P ij = P(X t = j | X t − 1 = i), and π i and π j are the equilibrium probabilities of being in states i and j, respectively ...
In a chemical reaction, chemical equilibrium is the state in which both the reactants and products are present in concentrations which have no further tendency to change with time, so that there is no observable change in the properties of the system. [1] This state results when the forward reaction proceeds at the same rate as the reverse ...
A gömböc (Hungarian: [ˈɡømbøt͡s]) is any member of a class of convex, three-dimensional and homogeneous bodies that are mono-monostatic, meaning that they have just one stable and one unstable point of equilibrium when resting on a flat surface. [1] The existence of this class was conjectured by the Russian mathematician Vladimir Arnold ...
In thermodynamics, the phase rule is a general principle governing multi-component, multi-phase systems in thermodynamic equilibrium.For a system without chemical reactions, it relates the number of freely varying intensive properties (F) to the number of components (C), the number of phases (P), and number of ways of performing work on the system (N): [1] [2] [3]: 123–125
In the history of thermodynamics, "On the Equilibrium of Heterogeneous Substances" is a 300-page paper written by American chemical physicist Willard Gibbs. It is one of the founding papers in thermodynamics , along with German physicist Hermann von Helmholtz 's 1882 paper " Thermodynamik chemischer Vorgänge ."
In physics, a homogeneous material or system has the same properties at every point; it is uniform without irregularities. [ 1 ] [ 2 ] A uniform electric field (which has the same strength and the same direction at each point) would be compatible with homogeneity (all points experience the same physics).
The word equilibrium implies a state of balance. Equilibrium thermodynamics, in origins, derives from analysis of the Carnot cycle. Here, typically a system, as cylinder of gas, initially in its own state of internal thermodynamic equilibrium, is set out of balance via heat input from a combustion reaction. Then, through a series of steps, as ...
Homogeneity and heterogeneity; only ' b ' is homogeneous Homogeneity and heterogeneity are concepts relating to the uniformity of a substance, process or image.A homogeneous feature is uniform in composition or character (i.e., color, shape, size, weight, height, distribution, texture, language, income, disease, temperature, radioactivity, architectural design, etc.); one that is heterogeneous ...