{"id": "card_thermo_first_law", "kind": "reference", "title": "The first law — energy is conserved", "body": "dU = dQ - dW: energy is conserved, counted now as heat and work. This is exactly the conserved energy Noether derives from time-translation symmetry - the same invariant, bookkept for a thermal system. Rests on Noether.", "source": {"label": "Narrow Highway — thermodynamics", "url": "", "authority_tier": "engine_derived"}, "shelf": "codex", "box": "thermodynamics", "bands": ["thermodynamics", "pillar", "first_law", "one map"], "subject": "The first law — energy is conserved", "connections": [{"to_card_id": "card_floor_thermodynamics", "relationship": "part_of", "evidence": "a law of thermodynamics (The first law)"}, {"to_card_id": "card_floor_noethers_theorem", "relationship": "connects_at", "evidence": "the first law is Noether's conserved energy, accounting heat and work"}], "author": "engine", "created_at": 0.0, "updated_at": 0.0, "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "generated": false, "call": "codex.thermodynamics", "facets": {"subject": ["first_law", "one map", "pillar"]}, "presentation": {"glyph": "•", "kind_label": "thermodynamics", "by": "Narrow Highway — thermodynamics", "authority": "engine_derived", "posted": "", "standing": ""}, "neighbors": [{"id": "card_floor_thermodynamics", "title": "Thermodynamics — the arrow and the one end", "relationship": "part of", "why": "a law of thermodynamics (The first law)", "href": "/card/card_floor_thermodynamics", "resolved": true}, {"id": "card_floor_noethers_theorem", "title": "Noether's theorem — symmetry is the source of conservation", "relationship": "connects at", "why": "the first law is Noether's conserved energy, accounting heat and work", "href": "/card/card_floor_noethers_theorem", "resolved": true}], "house": {"door": "FIND", "kind": "card", "trail": "connections", "seal": "/card/card_thermo_first_law", "next_step": {"do": "follow a connection: what this card rests on, and what rests on it", "door": "FIND", "tool": "card_connections", "params": {"id": "card_thermo_first_law"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}