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  2. Conservation of energy - Wikipedia

    en.wikipedia.org/wiki/Conservation_of_energy

    This is an accepted version of this page This is the latest accepted revision, reviewed on 4 December 2024. Law of physics and chemistry This article is about the law of conservation of energy in physics. For sustainable energy resources, see Energy conservation. Part of a series on Continuum mechanics J = − D d φ d x {\displaystyle J=-D{\frac {d\varphi }{dx}}} Fick's laws of diffusion Laws ...

  3. Conservation law - Wikipedia

    en.wikipedia.org/wiki/Conservation_law

    A local conservation law is usually expressed mathematically as a continuity equation, a partial differential equation which gives a relation between the amount of the quantity and the "transport" of that quantity. It states that the amount of the conserved quantity at a point or within a volume can only change by the amount of the quantity ...

  4. Noether's theorem - Wikipedia

    en.wikipedia.org/wiki/Noether's_theorem

    The global versions can be united into a single global conservation law: the conservation of the energy-momentum 4-vector. The local versions of energy and momentum conservation (at any point in space-time) can also be united, into the conservation of a quantity defined locally at the space-time point: the stress–energy tensor [ 11 ] : 592 ...

  5. Continuity equation - Wikipedia

    en.wikipedia.org/wiki/Continuity_equation

    For example, the stress–energy tensor is a second-order tensor field containing energy–momentum densities, energy–momentum fluxes, and shear stresses, of a mass-energy distribution. The differential form of energy–momentum conservation in general relativity states that the covariant divergence of the stress-energy tensor is zero: T μ ...

  6. Thermodynamic equations - Wikipedia

    en.wikipedia.org/wiki/Thermodynamic_equations

    The first law is the law of conservation of energy. The symbol δ {\displaystyle \delta } instead of the plain d, originated in the work of German mathematician Carl Gottfried Neumann [ 1 ] and is used to denote an inexact differential and to indicate that Q and W are path-dependent (i.e., they are not state functions ).

  7. Conserved current - Wikipedia

    en.wikipedia.org/wiki/Conserved_current

    The continuity equation for the conserved current is a statement of a conservation law. Examples of canonical conjugate quantities are: Time and energy - the continuous translational symmetry of time implies the conservation of energy; Space and momentum - the continuous translational symmetry of space implies the conservation of momentum

  8. Laws of thermodynamics - Wikipedia

    en.wikipedia.org/wiki/Laws_of_thermodynamics

    The first law of thermodynamics states that, when energy passes into or out of a system (as work, heat, or matter), the system's internal energy changes in accordance with the law of conservation of energy. The second law of thermodynamics states that in a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic ...

  9. First law of thermodynamics - Wikipedia

    en.wikipedia.org/wiki/First_law_of_thermodynamics

    The first law of thermodynamics for closed systems was originally induced from empirically observed evidence, including calorimetric evidence. It is nowadays, however, taken to provide the definition of heat via the law of conservation of energy and the definition of work in terms of changes in the external parameters of a system.