For inhomogeneous systems the enthalpy is the sum of the enthalpies of the composing subsystems:
2.
The entropy of inhomogeneous systems is the sum of the entropies of the various subsystems.
3.
This is a serious difficulty for attempts to define entropy for time-varying spatially inhomogeneous systems.
4.
The laws of thermodynamics hold rigorously for inhomogeneous systems even though they may be far from internal equilibrium.
5.
In complex inhomogeneous systems, such as simulations of membrane proteins in a lipid bilayer, equipartition artifacts are difficult to avoid and may simply be post-processed.
6.
Just as temperature may undefined for a sufficiently inhomogeneous system, so also may entropy be undefined for a system not in its own state of internal thermodynamic equilibrium.
7.
The calculating of excess chemical potential is not limited to homogeneous systems, but has also been extended to inhomogeneous systems by the Widom insertion method, or other NVE.
8.
One fundamental difference between equilibrium thermodynamics and non-equilibrium thermodynamics lies in the behaviour of inhomogeneous systems, which require for their study knowledge of rates of reaction which are not considered in equilibrium thermodynamics of homogeneous systems.
9.
Quantum mechanics prohibits it in a uniform ordinary superconductor, but it becomes possible in an inhomogeneous system, for example, if a vortex is placed on a boundary between two superconductors which are connected only by an extremely weak link ( also called a Josephson junction ); such a situation also occurs in some cases in polycrystalline samples on grain boundaries etc . At such superconducting boundaries the phase can have a discontinuous jump.
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