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Physics of many interacting particles
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic
Statistical_mechanics
Specific microscopic configuration of a thermodynamic system
In statistical mechanics, a microstate is a specific configuration of a system that describes the precise positions and momenta of all the individual
Microstate (statistical mechanics)
Microstate_(statistical_mechanics)
Function in thermodynamics and statistical physics
represent a particular statistical ensemble (which, in turn, corresponds to a particular free energy). The most common statistical ensembles have named
Partition function (statistical mechanics)
Partition_function_(statistical_mechanics)
Number of microstates for a given macrostate of a thermodynamic system
In statistical mechanics, multiplicity (also called statistical weight) refers to the number of microstates corresponding to a particular macrostate of
Multiplicity (statistical mechanics)
Multiplicity_(statistical_mechanics)
A list of notable textbooks in thermodynamics and statistical mechanics, arranged by category and date. Fermi, Enrico (1956). Thermodynamics (New ed.)
List of textbooks in thermodynamics and statistical mechanics
List_of_textbooks_in_thermodynamics_and_statistical_mechanics
Statistical mechanics of quantum-mechanical systems
Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems. It relies on constructing density matrices that describe
Quantum_statistical_mechanics
Measure of a system's order
In statistical mechanics, the correlation function is a measure of the order in a system, as characterized by a mathematical correlation function. Correlation
Correlation function (statistical mechanics)
Correlation_function_(statistical_mechanics)
Idealization of a large number of atomic-sized systems
system might be in. In other words, a statistical ensemble is a set of systems of particles used in statistical mechanics to describe a single system. The
Ensemble (mathematical physics)
Ensemble_(mathematical_physics)
Science concerned with physical bodies subjected to forces or displacements
Mechanics (from Ancient Greek μηχανική (mēkhanikḗ) 'of machines') is the area of physics concerned with the relationships between force, matter, and motion
Mechanics
Property of a thermodynamic system
introduced the concept of statistical disorder and probability distributions into a new field of thermodynamics, called statistical mechanics, and found the link
Entropy
Smooth approximation of one-hot arg max
which gives another interpretation for the limit behavior. In statistical mechanics, the softargmax function is known as the Boltzmann distribution
Softmax_function
Book by Josiah Willard Gibbs
Elementary Principles in Statistical Mechanics, published in March 1902, is a scientific treatise by Josiah Willard Gibbs which is considered to be the
Elementary Principles in Statistical Mechanics
Elementary_Principles_in_Statistical_Mechanics
Austrian mathematician and theoretical physicist (1844–1906)
as a measure of the statistical disorder of a system. Max Planck named the constant kB the Boltzmann constant. Statistical mechanics is one of the pillars
Ludwig_Boltzmann
Scientific subjects
physics include classical mechanics; thermodynamics and statistical mechanics; electromagnetism; relativity; quantum mechanics, atomic physics, and molecular
Branches_of_physics
Physical quantity of hot and cold
the kelvin has been defined through particle kinetic theory, and statistical mechanics. In the International System of Units (SI), the magnitude of the
Temperature
Concept in statistical mechanics
In statistical mechanics, universality is the observation that there are properties for a large class of systems that are independent of the dynamical
Universality (dynamical systems)
Universality_(dynamical_systems)
Branch of applied mathematics
have been extended to other areas of physics, such as statistical mechanics, continuum mechanics, classical field theory, and quantum field theory. Moreover
Mathematical_physics
Differentiating positive and negative zero
concept of negative zero also has some theoretical applications in statistical mechanics and other disciplines. It is claimed that the inclusion of signed
Signed_zero
Equation of the state of a hypothetical ideal gas
whether the universal or specific gas constant is being used. In statistical mechanics, the following molecular equation (i.e. the ideal gas law in its
Ideal_gas_law
Academic journal
result of the splitting of Physica in 1975. It is concerned with statistical mechanics and its applications, particularly random systems, fluids and soft
Physica_(journal)
Physics of heat, work, and temperature
formulations of thermodynamics emerged. Statistical thermodynamics, or statistical mechanics, concerns itself with statistical predictions of the collective motion
Thermodynamics
Truths and principles of the study of matter, space, time and energy
with quantum mechanics, gravitational singularities, and philosophical implications of cosmology are also investigated. Statistical mechanics: Relationship
Philosophy_of_physics
Physical constant in quantum mechanics
theory, Planck resorted to using the then-controversial theory of statistical mechanics, which he described as "an act of desperation". One of his new boundary
Planck_constant
Length scale which are visible to the naked eye
extends from macroscopic to microscopic viewpoints is histology. In statistical mechanics, a macroscopic quantity refers to averages of many particles, like
Macroscopic_scale
Mathematical technique
In statistical mechanics, the transfer-matrix method is a mathematical technique which is used to write the partition function into a simpler form. It
Transfer-matrix method (statistical mechanics)
Transfer-matrix_method_(statistical_mechanics)
Book by Leonard Susskind
classical mechanics, quantum mechanics, special relativity and classical field theory, general relativity, cosmology, and statistical mechanics. Videos
The_Theoretical_Minimum
Textbook by Herbert Callen
The second part of the text presents the foundations of classical statistical mechanics. Boltzmann's entropy formula is introduced and used to describe
Thermodynamics and an Introduction to Thermostatistics
Thermodynamics_and_an_Introduction_to_Thermostatistics
This is a list of notable textbooks on classical mechanics and quantum mechanics arranged according to level and surnames of the authors in alphabetical
List of textbooks on classical mechanics and quantum mechanics
List_of_textbooks_on_classical_mechanics_and_quantum_mechanics
Carlo in statistical physics refers to the application of the Monte Carlo method to problems in statistical physics, or statistical mechanics. The general
Monte Carlo method in statistical mechanics
Monte_Carlo_method_in_statistical_mechanics
1948 book written by Norbert Wiener
Beings. Introduction 1. Newtonian and Bergsonian Time 2. Groups and Statistical Mechanics 3. Time Series, Information, and Communication 4. Feedback and Oscillation
Cybernetics: Or Control and Communication in the Animal and the Machine
Cybernetics:_Or_Control_and_Communication_in_the_Animal_and_the_Machine
Branch of economic theory
the interactions between different economic agents. The use of statistical mechanics in economics involves applying concepts and methods from physics
Non-equilibrium_economics
Small localized object
Ivo; Sen, Siddhartha; Sexton, James (May 11, 2006). Elements of Statistical Mechanics: With an Introduction to Quantum Field Theory and Numerical Simulation
Particle
Stochastic forensics is inspired by the statistical mechanics method used in physics. Classical Newtonian mechanics calculates the exact position and momentum
Stochastic_forensics
Thermodynamical parameter of solids
{\alpha VK_{T}}{{\tilde {C}}_{V}}}.} Regarding Boltzmann-Gibbs (BG) statistical mechanics, it is reported in the literature that the Grüneisen parameter presents
Grüneisen_parameter
the number of identical processes. Statistical fluctuations are responsible for many results of statistical mechanics and thermodynamics, including phenomena
Statistical_fluctuations
Method to measure temperature quantitatively
Thermodynamics and statistical mechanics. New York [u.a.] : Springer, 2004. pp. 6~7. Carl S. Helrich (2009). Modern Thermodynamics with Statistical Mechanics. Berlin
Scale_of_temperature
(heat) entropy on the microscopic level are found in statistical thermodynamics and statistical mechanics. For most of the 20th century, textbooks tended to
Introduction_to_entropy
French theoretical physicist
French theoretical physicist. He is best known for his work in statistical mechanics, and is the eponym of Derrida plots, an analytical technique for
Bernard_Derrida
Indian theoretical physicist (1933–2026)
transitions. Pathria was also the author of a graduate textbook on statistical mechanics, whose fourth edition appeared in the year 2021. He also wrote a
Raj_Kumar_Pathria
Soviet mathematician and theoretical physicist (1909–1992)
significant contributions to quantum field theory, classical and quantum statistical mechanics, and the theory of dynamical systems; he was the recipient of the
Nikolay_Bogolyubov
Application of information theory to thermodynamics and statistical mechanics
(colloquially, MaxEnt thermodynamics) views equilibrium thermodynamics and statistical mechanics as inference processes. More specifically, MaxEnt applies inference
Maximum entropy thermodynamics
Maximum_entropy_thermodynamics
Examination
fixed axis dynamics of systems of particles central forces and celestial mechanics three-dimensional particle dynamics Lagrangian and Hamiltonian formalism
GRE_Physics_Test
Description of large objects' physics
whose speed is greater than a small fraction of the speed of light. Statistical mechanics, which provides a framework for relating the microscopic properties
Classical_mechanics
American physicist (1881–1948)
mathematical physicist and physical chemist who made many contributions to statistical mechanics and theoretical cosmology. He was a professor at the California
Richard_C._Tolman
Series of textbooks by Arnold Sommerfeld
includes the volumes Mechanics, Mechanics of Deformable Bodies, Electrodynamics, Optics, Thermodynamics and Statistical Mechanics, and Partial Differential
Lectures on Theoretical Physics
Lectures_on_Theoretical_Physics
Mathematical entity to describe the probability of each possible measurement on a system
quantum state is a statistical ensemble of pure states (see Quantum statistical mechanics). Mixed states arise in quantum mechanics in two different situations:
Quantum_state
Formulation of quantum mechanics
The path-integral formulation of quantum mechanics generalizes the action principle of classical mechanics. It replaces the classical notion of a single
Path-integral_formulation
Part of the history of physics
Statistical Mechanics, stating that the form of H will be recognized as that of entropy as defined in certain formulations of statistical mechanics where
History_of_entropy
Israeli chemist
the use of information theory to better understand and advance statistical mechanics and thermodynamics. Books written by Arieh Ben-Naim: Water and Aqueous
Arieh_Ben-Naim
American historian of science (born 1935)
American historian of science known particularly for his work on statistical mechanics and geophysics. He was a professor at the University of Maryland
Stephen_G._Brush
Description of physical properties at the atomic and subatomic scale
Quantum mechanics, also known as quantum physics, is the fundamental physical theory that describes the behavior of matter and of light; the behaviors
Quantum_mechanics
Branch of physics
Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. Originally applied
Fluid_mechanics
Study of forces and their effect on motion
classical mechanics, along with statics and kinematics. The fundamental principle of dynamics is linked to Newton's second law. In classical mechanics, rigid
Dynamics_(mechanics)
American mathematician
mathematician, specializing in probability theory on graphs, combinatorics, statistical mechanics, ergodic theory and harmonic analysis. Lyons graduated with B.A
Russell_Lyons
Physical law for entropy and heat
3390/e21090890. PMC 7515426. "2. The Statistical Description of Physical Systems — Introduction to Statistical Mechanics". web.stanford.edu. Retrieved 2025-10-20
Second_law_of_thermodynamics
American scientist (1839–1903)
Boltzmann, he created statistical mechanics (a term that he coined), explaining the laws of thermodynamics as consequences of the statistical properties of ensembles
Josiah_Willard_Gibbs
Tatjana Ehrenfest–Afanassjewa publish their classical review on the statistical mechanics of Boltzmann, Begriffliche Grundlagen der statistischen Auffassung
Timeline_of_thermodynamics
Scientific field of study
literate in them. These include classical mechanics, quantum mechanics, thermodynamics and statistical mechanics, electromagnetism, and special relativity
Physics
Concept
or impossible. In statistical mechanics, entropy is formulated as a statistical property using probability theory. The statistical entropy perspective
Entropy (statistical thermodynamics)
Entropy_(statistical_thermodynamics)
German-born theoretical physicist (1879–1955)
middle part of his career, Einstein made important contributions to statistical mechanics and quantum theory. Especially notable was his work on the quantum
Albert_Einstein
Interpretation of quantum mechanics
The many-worlds interpretation (MWI) is an interpretation of quantum mechanics that asserts that the universal wave function is objectively real, and
Many-worlds_interpretation
Framework to describe phase transitions
well as non-equilibrium phase transitions. A SFT is any model in statistical mechanics where the degrees of freedom comprise a field or fields. In other
Statistical_field_theory
Distribution of an uncertain quantity
used to represent initial beliefs about an uncertain parameter, in statistical mechanics the a priori probability is used to describe the initial state of
Prior_probability
Relation of magnetization to applied magnetic field and temperature
pp. 304. ISBN 0-471-41526-X. Van Vleck, J. H. (1978-07-14). "Quantum Mechanics: The Key to Understanding Magnetism". Science. 201 (4351): 113–120. doi:10
Curie's_law
Mathematical model of ferromagnetism in statistical mechanics
and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent magnetic
Ising_model
State of matter
particles (molecules and atoms) which make up the [gas] system. In statistical mechanics, temperature is the measure of the average kinetic energy stored
Gas
British mathematical physicist (1889–1944)
University Press. 1929. with E. A. Guggenheim: Statistical thermodynamics: a version of statistical mechanics for students of physics and chemistry. Cambridge
Ralph_Fowler
Integral transform useful in probability theory, physics, and engineering
\varphi }{s^{2}+\omega ^{2}}}\right\}=\cos {(\omega t+\varphi )}.} In statistical mechanics, the Laplace transform of the density of states g ( E ) {\displaystyle
Laplace_transform
Property of measure-preserving dynamical systems
lie in statistical physics, where Ludwig Boltzmann formulated the ergodic hypothesis in connection with the foundations of statistical mechanics. Ergodicity
Ergodicity
Heat required to raise the temperature of a given unit of mass of a substance
Material properties (thermodynamics) Quantum statistical mechanics R-value (insulation) Statistical mechanics Table of specific heat capacities Thermal mass
Specific_heat_capacity
Counterintuitive result in probability
foundations of statistical mechanics. There is straightforward proof of this theorem. As an introduction, recall that if two events are statistically independent
Infinite_monkey_theorem
American physicist
liquids, the fractional quantum Hall effect, and exact solutions in statistical mechanics. Shankar was born in New Delhi into a Tamil family. His elder brother
Ramamurti_Shankar
Peer-reviewed scientific journal
The Journal of Statistical Mechanics: Theory and Experiment is a peer-reviewed scientific journal published by the International School for Advanced Studies
Journal of Statistical Mechanics: Theory and Experiment
Journal_of_Statistical_Mechanics:_Theory_and_Experiment
Mathematical structures that allow quantum mechanics to be explained
formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism
Mathematical formulation of quantum mechanics
Mathematical_formulation_of_quantum_mechanics
Historical development of physics
and statistical mechanics were discovered. At the beginning of the 20th century, physics was transformed by the discoveries of quantum mechanics, relativity
History_of_physics
Regular infinite tree structure used in statistical mechanics
In statistical mechanics and mathematics, the Bethe lattice (also called a regular tree) is an infinite symmetric regular tree where all vertices have
Bethe_lattice
Wigner distribution function in physics as opposed to in signal processing
Eugene Wigner in 1932 to study quantum corrections to classical statistical mechanics. The goal was to link the wavefunction that appears in the Schrödinger
Wigner quasiprobability distribution
Wigner_quasiprobability_distribution
theories of relativity. He also made important contributions to statistical mechanics, especially by his treatment of Brownian motion, his resolution
List of scientific publications by Albert Einstein
List_of_scientific_publications_by_Albert_Einstein
Chinese-American physicist (1922–2025)
Chinese-American theoretical physicist who made significant contributions to statistical mechanics, integrable systems, gauge theory, particle physics and condensed
Yang_Chen-Ning
Overview of and topical guide to physics
(NMR, PET scans, and so on), radiotherapy, and nuclear medicine. Statistical mechanics – the branch of physics that studies any physical system that has
Outline_of_physics
Swedish theoretical physicist
entropy applied to the measurement process in quantum theory and statistical mechanics," on May 29, 1974. His PhD thesis summarized the contents of some
Göran_Lindblad_(physicist)
Austrian theoretical physicist (1880–1933)
theoretical physicist who made major contributions to statistical mechanics and its relation to quantum mechanics, including the theory of phase transition and
Paul_Ehrenfest
Observational basis of thermodynamics
and Statistical Mechanics, Cambridge University Press, London, pp. 4, 8, 68, 86, 97, 311. Ben-Naim, A. (2008). A Farewell to Entropy: Statistical Thermodynamics
Laws_of_thermodynamics
One area where unequal probabilities were indeed well known was statistical mechanics, where Ludwig Boltzmann had, in the context of his H-theorem of
History_of_information_theory
Concept in quantum mechanics of perfectly substitutable particles
fact that particles can be identical has important consequences in statistical mechanics, where calculations rely on probabilistic arguments, which are sensitive
Indistinguishable_particles
Canadian-American physicist and academic
towards the statistical mechanics of gases, he presented multiple approaches, including the "Formalism" for quantum statistical mechanics of gases in
André_LeClair
Indian theoretical physicist
Nonequilibrium Statistical Mechanics. CRC Press. ISBN 978-1420074192. Duenweg, B (2008). "Book review: Elements of Nonequilibrium Statistical Mechanics". Soft
V._Balakrishnan_(physicist)
2007 textbook series by Mehran Kardar
Mehran (2007). Statistical Physics of Fields. Cambridge University Press. ISBN 978-0-521-87341-3. OCLC 920137477. Statistical Mechanics I at MIT OpenCourseWare
Statistical Physics of Particles
Statistical_Physics_of_Particles
Formulation of classical mechanics in terms of Hilbert spaces
formulations of classical mechanics in what follows. Statistical mechanics describes macroscopic systems in terms of statistical ensembles, such as the macroscopic
Koopman–von Neumann classical mechanics
Koopman–von_Neumann_classical_mechanics
French mathematical physicist
(born 1948) is a French mathematical physicist, specializing in statistical mechanics, stochastic processes, and chaos theory. In 1978, Collet received
Pierre_Collet_(physicist)
Mathematical model which approximates the behavior of real gases
simplified equation of state, and is amenable to analysis under statistical mechanics. The requirement of zero interaction can often be relaxed if, for
Ideal_gas
Branch of astronomy
Celestial mechanics is the branch of astronomy that deals with the motions and gravitational interactions of objects in outer space. Historically, celestial
Celestial_mechanics
Type of stochastic recurrent neural network
practical problems. They are named after the Boltzmann distribution in statistical mechanics, which is used in their sampling function. They were heavily popularized
Boltzmann_machine
Branch of thermodynamics
continuum thermomechanics, which evolved completely independently of statistical mechanics and maximum-entropy principles. To describe deviation of the thermodynamic
Non-equilibrium thermodynamics
Non-equilibrium_thermodynamics
Branch of mathematics concerning probability
complex systems given only partial knowledge of their state, as in statistical mechanics or sequential estimation. A great discovery of twentieth-century
Probability_theory
Belgian physical chemist (1917–2003)
Austin, in 1967, he co-founded the Center for Thermodynamics and Statistical Mechanics, now the Center for Complex Quantum Systems. In that year, he also
Ilya_Prigogine
French mathematician (1875–1941)
establishing the validity of Willard Gibbs' work on the foundations of statistical mechanics. The notions of average and measure were urgently needed to provide
Henri_Lebesgue
Process that cannot be undone or reversed
2009.06.027. Lucia, U (2008). "Statistical approach of the irreversible entropy variation". Physica A: Statistical Mechanics and Its Applications. 387 (14):
Irreversible_process
Scottish physicist and mathematician (1831–1879)
realised by Isaac Newton. Maxwell was also key in the creation of statistical mechanics. Maxwell graduated from Trinity College, Cambridge, in 1854, where
James_Clerk_Maxwell
Vector relating the initial and the final positions of a moving point
In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing
Displacement_(geometry)
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