path-independent
|path-in-de-pen-dent|
🇺🇸
/ˌpæθ ɪnˈdɛpəndənt/
🇬🇧
/ˌpɑːθ ɪnˈdep(ə)ndənt/
doesn't depend on the route
Etymology
'path-independent' originates from English, specifically a compound of 'path' and 'independent', where 'path' ultimately comes from Old English 'pæð' meaning 'way' and 'independent' comes from Late Latin 'independens' (in- 'not' + dependere 'to hang from').
'path' changed from Old English 'pæð' (meaning 'way') into modern English 'path', and 'independent' came from Late Latin 'independens' via Old French and Middle English into modern English; the modern compound 'path-independent' was formed in English by combining these two elements to describe quantities not depending on a route.
Initially the components meant 'way' and 'not depending (hanging from)', but together they evolved into the technical sense 'not depending on the path/route' used in mathematics and physics.
Meanings by Part of Speech
Adjective 1
in mathematics, especially vector calculus, describing a quantity (e.g., a line integral) whose value depends only on the endpoints of a path and not on the particular route taken; characteristic of a conservative field.
The line integral of a conservative vector field is path-independent: its value depends only on the endpoints.
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Adjective 2
in physics and thermodynamics, describing a state function (e.g., internal energy) whose change depends only on the initial and final states, not on the process or path taken between them.
Internal energy is a path-independent state function, so its change depends only on the initial and final states, not on how the system changed between them.
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Last updated: 2025/09/09 01:10