Energy conservation is a consequence of time-translation symmetry
Energy conservation is indeed a direct consequence of time-translation symmetry, a foundational principle established by Noether's theorem.
The retrieved papers, particularly those discussing Noether's theorem and its applications in physics and thermodynamics (such as papers [0], [1], and [4]), consistently support the well-established physical principle that continuous time-translation symmetry implies the conservation of energy.
Lorenzo Fatibene, Mauro Francaviglia, Silvio Mercadante. Noether Symmetries and Covariant Conservation Laws in Classical, Relativistic and Quantum Physics. 2010. https://doi.org/10.3390/sym2020970
Paper [0] reviews Noether's theorem and the foundational connection between symmetries, including time translation, and conservation laws such as energy.
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Pizlo Z, de Barros JA. The Concept of Symmetry and the Theory of Perception.. 2021. https://doi.org/10.3389/fncom.2021.681162
Paper [1] discusses how Emmy Noether's mathematical theorems connected symmetries of physical laws to conservation laws.
Bravetti A, García-Ariza MÁ, Tapias D. Thermodynamic Entropy as a Noether Invariant from Contact Geometry.. 2023. https://doi.org/10.3390/e25071082
Paper [4] uses a formulation of Noether's theorem to derive a relation between thermodynamic entropy and the Noether invariant associated with time-translational symmetry.
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