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  1. Chemical Potential

    Linked via "system"

    The chemical potential ($\mu$), often described thermodynamically as the partial molar Gibbs free energy ($G$), quantifies the change in the thermodynamic potential of a system/) when the number of moles of a specific component/) is varied while keeping temperature, pressure, and the number of moles of all other components constant. In condensed matter physics and [quantum stati…

  2. Chemical Potential

    Linked via "system"

    Thermodynamic Definition and Derivatives
    Formally, for a system/) with energy $U$, entropy $S$, volume-and particle number $N$, the fundamental thermodynamic relation is often expressed in terms of the Gibbs free energy $G$ as:
    $$dG = -S dT + V dP + \mu dN$$
    From this, the chemical potential is derived as:

  3. Chemical Potential

    Linked via "systems"

    Chemical Potential in Non-Equilibrium Systems
    While typically defined for systems/) at thermal equilibrium, the concept of chemical potential is extended to local equilibrium descriptions in non-uniform or time-dependent systems/). In these scenarios, one speaks of a local chemical potential, $\mu(\mathbf{r}, t)$.
    A notable, if controversial, extension of this concept arises in the study of [lipid bilaye…

  4. Gradient Operator

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    Gradient and Thermodynamics
    In thermodynamics, the gradient operator plays a subtle role in defining thermal diffusion tendencies. While heat flux ($\mathbf{q}$) is conventionally described by Fourier's Law ($\mathbf{q} = -k \nabla T$, where $T$ is temperature), the application of the gradient to entropy density ($\eta$) yields the Entropic Drive Vector ($\nab…

  5. Kinetic Term

    Linked via "system"

    The kinetic term in theoretical physics (especially within the framework of Lagrangian formalism or Hamiltonian formalism), represents the component of the action/) or energy associated with the motion or dynamical evolution of a system/). It is fundamentally characterized by its dependence on the time derivative (or [spatial gradient](/entries/spatial…