Tolman–Ehrenfest effect

E145217

The Tolman–Ehrenfest effect is a relativistic thermodynamic phenomenon stating that, in a system at thermal equilibrium within a gravitational field, temperature varies with gravitational potential so that hotter regions occur deeper in the gravitational well.

All labels observed (7)

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Statements (44)

Predicate Object
instanceOf physical phenomenon
relativistic thermodynamic effect
appliesTo systems in static gravitational fields
systems in thermal equilibrium in curved spacetime
assumes general relativistic description of gravity
global thermal equilibrium
static spacetime metric
clarifies relationship between temperature and time dilation
compatibleWith gravitational time dilation
local validity of special relativity
context curved spacetime thermodynamics
equilibrium of self-gravitating systems
contrastsWith naive Newtonian expectation of uniform temperature at equilibrium in a gravitational field
describes temperature distribution in a gravitational field at thermal equilibrium
explains how local temperature must vary to maintain equilibrium in gravity
field general relativity
statistical mechanics
thermodynamics
formulatedBy Paul Ehrenfest
Richard C. Tolman
hasAlternativeName Tolman–Ehrenfest effect
surface form: Tolman law of temperature in a gravitational field

Tolman–Ehrenfest effect
surface form: Tolman temperature relation
hasConsequence thermodynamic equilibrium is frame and metric dependent
uniform temperature in a gravitational field is incompatible with full relativistic equilibrium
holdsWhen no heat flow occurs in the system
implies hotter regions occur deeper in a gravitational well at equilibrium
involvesQuantity gravitational potential
local temperature
metric component g00
proper time
mathematicalForm T(r)·sqrt(g00(r)) = constant in static spacetime
predicts temperature increases with depth in a gravitational potential well at equilibrium
relatedTo Einstein field equations
Tolman–Ehrenfest effect self-linksurface differs
surface form: Tolman law

Tolman–Ehrenfest effect self-linksurface differs
surface form: Tolman temperature gradient

equivalence principle
gravitational redshift
relativistic thermodynamic equilibrium
statesThat temperature varies with gravitational potential in thermal equilibrium
usedIn analysis of thermal radiation in gravitational fields
black hole thermodynamics
cosmological thermodynamics
relativistic stellar structure models
yearProposed 1930

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Referenced by (7)

Full triples — surface form annotated when it differs from this entity's canonical label.

Richard C. Tolman notableConcept Tolman–Ehrenfest effect
Tolman knownFor Tolman–Ehrenfest effect
subject surface form: Richard C. Tolman
this entity surface form: Tolman relation in relativistic thermodynamics
Tolman–Ehrenfest effect relatedTo Tolman–Ehrenfest effect self-linksurface differs
this entity surface form: Tolman temperature gradient
Tolman–Ehrenfest effect relatedTo Tolman–Ehrenfest effect self-linksurface differs
this entity surface form: Tolman law
Tolman–Ehrenfest effect hasAlternativeName Tolman–Ehrenfest effect
this entity surface form: Tolman temperature relation
Tolman–Ehrenfest effect hasAlternativeName Tolman–Ehrenfest effect
this entity surface form: Tolman law of temperature in a gravitational field
Paul Ehrenfest notableWork Tolman–Ehrenfest effect
this entity surface form: Ehrenfest–Tolman effect