In physics, the Boltzmann factor is a weighting factor that determines the relative probability of a state i in a multi-state system in thermodynamic equilibrium at temperature T. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. In Thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium Mechanical equilibrium, and Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature
Where kB is Boltzmann's constant, and Ei is the energy of state i. Bridge from macroscopic to microscopic physics Boltzmann's constant k is a bridge between Macroscopic and microscopic physics In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός The ratio of the probabilities of two states is given by the ratio of their Boltzmann factors.
The Boltzmann factor is not a probability by itself, because it is not normalized. Probability is the likelihood or chance that something is the case or will happen To normalize the Boltzmann factor into a probability, one divides it by the sum Z of the Boltzmann factors of all possible states of a system, which is called the partition function. In Statistical mechanics, the partition function Z is an important quantity that encodes the statistical properties of a system in Thermodynamic This gives the Boltzmann distribution. WikipediaWikiProject Probability#Standards for a discussion of standards used for probability distribution articles such as this one
From the Boltzmann factor it is possible to derive the Maxwell-Boltzmann statistics, Bose-Einstein statistics, and Fermi-Dirac statistics that govern classical particles as well as quantum mechanical bosons, and fermions, respectively. In Statistical mechanics, Maxwell–Boltzmann statistics describes the statistical distribution of material particles over various energy states in Thermal equilibrium In Statistical mechanics, Bose - Einstein statistics (or more colloquially B-E statistics determines the statistical distribution of In Statistical mechanics, Fermi-Dirac statistics is a particular case of Particle statistics developed by Enrico Fermi and Paul Dirac that A subatomic particle is an elementary or composite Particle smaller than an Atom. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons In Particle physics, bosons are particles which obey Bose-Einstein statistics; they are named after Satyendra Nath Bose and Albert Einstein In Particle physics, fermions are particles which obey Fermi-Dirac statistics; they are named after Enrico Fermi.
See also
- Boltzmann relation (plasma physics)
References
- Charles Kittel and Herbert Kroemer, Thermal Physics, 2nd ed. In a plasma, the Boltzmann relation connects the electron density n e to the plasma potential &phipl as follows n (Freeman & Co. : New York, 1980).
External links
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