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1. Chemical Potential

   Linked via "particle number"

   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:

2. Phase Space

   Linked via "particle number"

   Microstates and Ensembles
   In statistical mechanics, the system's state is specified by macroscopic variables (e.g., energy $E$, volume $V$, particle number $N$). The corresponding set of all possible microscopic states $(\mathbf{q}, \mathbf{p})$ that are consistent with these constraints forms a region or hypersurface within the full phase space.
   The thermodynamic probability, $\Omega$, is proportional to the [volume of this ac…