Quantum statistical mechanicsStatistical mechanics of quantum-mechanical systems ThermodynamicsThe classical Carnot heat engine Branches Classical Statistical Chemical Quantum thermodynamics Equilibrium / Non-equilibrium Laws Zeroth First Second Third Systems Closed system Open system Isolated system State Equation of state Ideal gas Real gas State of matter Phase (matter) Equilibrium Control volume Instruments Processes Isobaric Isochoric Isothermal Adiabatic Isentropic Isenthalpic Quasistatic Polytropic Free expansion Reversibility Irreversibility Endoreversibility Cycles Heat engines Heat pumps Thermal efficiency System propertiesNote: Conjugate variables in italics Property diagrams Intensive and extensive properties Process functions Work Heat Functions of state Temperature / Entropy (introduction) Pressure / Volume Chemical potential / Particle number Vapor quality Reduced properties Material properties Property databases Specific heat capacity c = {\displaystyle c=} T {\displaystyle T} ∂ S {\displaystyle \partial S} N {\displaystyle N} ∂ T {\displaystyle \partial T} Compressibility β = − {\displaystyle \beta =-} 1 {\displaystyle 1} ∂ V {\displaystyle \partial V} V {\displaystyle V} ∂ p {\displaystyle \partial p} Thermal expansion α = {\displaystyle \alpha =} 1 {\displaystyle 1} ∂ V {\displaystyle \partial V} V {\displaystyle V} ∂ T {\displaystyle \partial T} Equations Carnot's theorem Clausius theorem Fundamental relation Ideal gas law Maxwell relations Onsager reciprocal relations Bridgman's equations Table of thermodynamic equations Potentials Free energy Free entropy Internal energy U ( S , V ) {\displaystyle U(S,V)} Enthalpy H ( S , p ) = U + p V {\displaystyle H(S,p)=U+pV} Helmholtz free energy A ( T , V ) = U − T S {\displaystyle A(T,V)=U-TS} Gibbs free energy G ( T , p ) = H − T S {\displaystyle G(T,p)=H-TS} HistoryCulture History General Entropy Gas laws "Perpetual motion" machines Philosophy Entropy and time Entropy and life Brownian ratchet Maxwell's demon Heat death paradox Loschmidt's paradox Synergetics Theories Caloric theory Vis viva ("living force") Mechanical equivalent of heat Motive power Key publications An Inquiry Concerning theSource ...
Statistical mechanicsIn physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in a wide variety of fields such as biology, neuroscience, computer science, information theory and sociology.EntropyProperty of a thermodynamic system
Thermal equilibriumTwo physical systems are in thermal equilibrium if there is no net flow of thermal energy between them when they are connected by a path permeable to heat. Thermal equilibrium obeys the zeroth law of thermodynamics. A system is said to be in thermal equilibrium with itself if the temperature within the system is spatially uniform and temporally constant. Systems in thermodynamic equilibrium are always in thermal equilibrium, but the converse is not always true.ThermodynamicsPhysics of heat, work, and temperature ThermodynamicsThe classical Carnot heat engine Branches Classical Statistical Chemical Quantum thermodynamics Equilibrium / Non-equilibrium Laws Zeroth First Second Third Systems Closed system Open system Isolated system State Equation of state Ideal gas Real gas State of matter Phase (matter) Equilibrium Control volume Instruments Processes Isobaric Isochoric Isothermal Adiabatic Isentropic Isenthalpic Quasistatic Polytropic Free expansion Reversibility Irreversibility Endoreversibility Cycles Heat engines Heat pumps Thermal efficiency System propertiesNote: Conjugate variables in italics Property diagrams Intensive and extensive properties Process functions Work Heat Functions of state Temperature / Entropy (introduction) Pressure / Volume Chemical potential / Particle number Vapor quality Reduced properties Material properties Property databases Specific heat capacity c = {\displaystyle c=} T {\displaystyle T} ∂ S {\displaystyle \partial S} N {\displaystyle N} ∂ T {\displaystyle \partial T} Compressibility β = − {\displaystyle \beta =-} 1 {\displaystyle 1} ∂ V {\displaystyle \partial V} V {\displaystyle V} ∂ p {\displaystyle \partial p} Thermal expansion α = {\displaystyle \alpha =} 1 {\displaystyle 1} ∂ V {\displaystyle \partial V} V {\displaystyle V} ∂ T {\displaystyle \partial T} Equations Carnot's theorem Clausius theorem Fundamental relation Ideal gas law Maxwell relations Onsager reciprocal relations Bridgman's equations Table of thermodynamic equations Potentials Free energy Free entropy Internal energy U ( S , V ) {\displaystyle U(S,V)} Enthalpy H ( S , p ) = U + p V {\displaystyle H(S,p)=U+pV} Helmholtz free energy A ( T , V ) = U − T S {\displaystyle A(T,V)=U-TS} Gibbs free energy G ( T , p ) = H − T S {\displaystyle G(T,p)=H-TS} HistoryCulture History General Entropy Gas laws "Perpetual motion" machines Philosophy Entropy and time Entropy and life Brownian ratchet Maxwell's demon Heat death paradox Loschmidt's paradox Synergetics Theories Caloric theory Vis viva ("living force") Mechanical equivalent of heat Motive power Key publications An Inquiry Concerning theSource ...
TemperaturePhysical quantity of hot and coldIn classical thermodynamics and kinetic theory, temperature reflects the average kinetic energy of the particles in a system, providing a quantitative measure of how energy is distributed among microscopic degrees of freedom. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied on various reference points and thermometric substances for definition.PhysicsPhysics is the scientific study of matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. It is one of the most fundamental scientific disciplines. A scientist who specializes in the field of physics is called a physicist. Physics is one of the oldest academic disciplines.Eigenstate thermalization hypothesisThe eigenstate thermalization hypothesis (ETH) is a set of ideas which purports to explain when and why an isolated quantum mechanical system can be accurately described using equilibrium statistical mechanics. In particular, it is devoted to understanding how systems which are initially prepared in far-from-equilibrium states can evolve in time to a state which appears to be in thermal equilibrium.
EngineeringEngineering is the practice of systematically applying natural science and mathematics to design and improve systems, devices, or processes that solve problems under constraints. It is typically motivated by satisfying human needs, resulting in creations such as bridges, engines, smartphones, pacemakers, the internet, spacecraft, and washing machines.
ScienceSystematic endeavour to gain knowledgeScience is a systematic discipline that builds and organises knowledge in the form of testable explanations about nature and society. It is driven by the scientific method: an empirical cycle that typically involves making observations, producing hypotheses, testing them with evidence, and drawing conclusions.
Equipartition theoremIn classical statistical mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition.
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