The principle of microscopic reversibility in physics and chemistry is twofold:
First, it states that the microscopic detailed dynamics of particles and fields is time-reversible because the microscopic equations of motion are symmetric with respect to inversion in time (T-symmetry);
Second, it relates to the statistical description of the kinetics of macroscopic or mesoscopic systems as an ensemble of elementary processes: collisions, elementary transitions or reactions. For these processes, the consequence of the microscopic T-symmetry is: Corresponding to every individual process there is a reverse process, and in a state of equilibrium the average rate of every process is equal to the average rate of its reverse process.
The idea of microscopic reversibility was born together with physical kinetics. In 1872, Ludwig Boltzmann represented kinetics of gases as statistical ensemble of elementary collisions. Equations of mechanics are reversible in time, hence, the reverse collisions obey the same laws. This reversibility of collisions is the first example of microreversibility. According to Boltzmann, this microreversibility implies the principle of detailed balance for collisions: at the equilibrium ensemble each collision is equilibrated by its reverse collision. These ideas of Boltzmann were analyzed in detail and generalized by Richard C. Tolman.
In chemistry, J. H. van't Hoff (1884) came up with the idea that equilibrium has dynamical nature and is a result of the balance between the forward and backward reaction rates. He did not study reaction mechanisms with many elementary reactions and could not formulate the principle of detailed balance for complex reactions. In 1901, Rudolf Wegscheider introduced the principle of detailed balance for complex chemical reactions. He found that for a complex reaction the principle of detailed balance implies important and non-trivial relations between reaction rate constants for different reactions.
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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. 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.
Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. The term law has diverse usage in many cases (approximate, accurate, broad, or narrow) across all fields of natural science (physics, chemistry, astronomy, geoscience, biology). Laws are developed from data and can be further developed through mathematics; in all cases they are directly or indirectly based on empirical evidence.
We explore statistical physics in both classical and open quantum systems. Additionally, we will cover probabilistic data analysis that is extremely useful in many applications.
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