Ehrenfest equations
E735843
The Ehrenfest equations are relations in thermodynamics that describe how phase transition properties change with pressure and temperature, particularly for second-order phase transitions.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Ehrenfest equations canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T8490721 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Ehrenfest equations Context triple: [Paul Ehrenfest, notableWork, Ehrenfest equations]
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A.
Liouville–von Neumann equation
The Liouville–von Neumann equation is the fundamental quantum-mechanical evolution equation governing the time dependence of the density operator, generalizing the Schrödinger equation to mixed states and open-system dynamics.
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B.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
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C.
Bhabha–Corben equations
The Bhabha–Corben equations are relativistic wave equations in quantum electrodynamics that describe the dynamics of spinning charged particles, developed by physicists Homi J. Bhabha and H. C. Corben.
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D.
Boltzmann–Kac equation
The Boltzmann–Kac equation is a kinetic equation in statistical mechanics that models the evolution of the velocity distribution of particles in a gas, providing a probabilistic framework related to the classical Boltzmann equation.
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E.
Landau–Lifshitz equations
The Landau–Lifshitz equations are fundamental differential equations in theoretical physics that describe the dynamics of magnetization in ferromagnets and, more broadly, the behavior of fields in relativistic and nonrelativistic continuum theories.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Ehrenfest equations Target entity description: The Ehrenfest equations are relations in thermodynamics that describe how phase transition properties change with pressure and temperature, particularly for second-order phase transitions.
-
A.
Liouville–von Neumann equation
The Liouville–von Neumann equation is the fundamental quantum-mechanical evolution equation governing the time dependence of the density operator, generalizing the Schrödinger equation to mixed states and open-system dynamics.
-
B.
Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
-
C.
Bhabha–Corben equations
The Bhabha–Corben equations are relativistic wave equations in quantum electrodynamics that describe the dynamics of spinning charged particles, developed by physicists Homi J. Bhabha and H. C. Corben.
-
D.
Boltzmann–Kac equation
The Boltzmann–Kac equation is a kinetic equation in statistical mechanics that models the evolution of the velocity distribution of particles in a gas, providing a probabilistic framework related to the classical Boltzmann equation.
-
E.
Landau–Lifshitz equations
The Landau–Lifshitz equations are fundamental differential equations in theoretical physics that describe the dynamics of magnetization in ferromagnets and, more broadly, the behavior of fields in relativistic and nonrelativistic continuum theories.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
equation in thermodynamics
ⓘ
phase transition relation ⓘ thermodynamic relation ⓘ |
| appliesTo |
continuous phase transitions
ⓘ
second-order phase transitions ⓘ |
| assumes |
continuity of Gibbs free energy across the phase boundary
ⓘ
continuity of first derivatives of Gibbs free energy for second-order transitions ⓘ reversible processes at the phase boundary ⓘ |
| basedOn | Gibbs free energy NERFINISHED ⓘ |
| category | thermodynamic equations of state ⓘ |
| characterizes | second-order phase transition via discontinuity of second derivatives of Gibbs free energy ⓘ |
| comparedTo | Clapeyron equation NERFINISHED ⓘ |
| describes |
behavior of phase transitions under changes of pressure and temperature
ⓘ
discontinuities in response functions at a phase transition ⓘ |
| field |
statistical mechanics
ⓘ
thermodynamics ⓘ |
| generalizes | Clapeyron equation to second-order transitions ⓘ |
| hasForm |
dT_c/dp = (V_2 - V_1)/(S_2 - S_1) for a phase transition
ⓘ
dT_c/dp = (κ_{T2} - κ_{T1})/(α_2 - α_1) T_c for a second-order transition ⓘ dT_c/dp = T_c (α_2 - α_1)/(C_{p2} - C_{p1}) for a second-order transition ⓘ |
| hasVariable |
molar entropy
ⓘ
molar volume ⓘ pressure ⓘ temperature ⓘ |
| historicalContext | introduced in early 20th century ⓘ |
| involves |
entropy
ⓘ
heat capacity at constant pressure ⓘ isothermal compressibility ⓘ pressure ⓘ thermal expansion coefficient ⓘ transition temperature ⓘ volume ⓘ |
| namedAfter | Paul Ehrenfest NERFINISHED ⓘ |
| relates |
changes in transition temperature to pressure
ⓘ
critical exponents approximately in mean-field theories ⓘ heat capacity discontinuity at a phase transition ⓘ isothermal compressibility discontinuity at a phase transition ⓘ slope of phase boundary in pressure–temperature space ⓘ thermal expansion coefficient discontinuity at a phase transition ⓘ |
| requires | equilibrium between phases ⓘ |
| usedFor | classifying phase transitions by order ⓘ |
| usedIn |
analysis of lambda transitions
ⓘ
condensed matter physics ⓘ equilibrium thermodynamics ⓘ materials science ⓘ solid-state physics ⓘ study of critical phenomena ⓘ |
How these facts were elicited
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Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Ehrenfest equations Description of subject: The Ehrenfest equations are relations in thermodynamics that describe how phase transition properties change with pressure and temperature, particularly for second-order phase transitions.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.