Particle reservoir

A particle reservoir is a thermodynamic system so large that it can exchange particles with another system without significantly changing its own chemical potential $\mu$.

Role in grand canonical ensemble

When a system is in contact with both a heat bath (temperature $T$) and a particle reservoir (chemical potential $\mu$), it is described by the grand canonical ensemble .

The reservoir imposes a fixed chemical potential, while the system’s particle number $N$ fluctuates.

Mathematical idealization

A reservoir has effectively infinite capacity:

• Adding or removing particles does not change $\mu$.
• The combined system (reservoir + small system) is isolated.
• At equilibrium, chemical potentials equalize.

Grand canonical distribution

The probability of a microstate with energy $E$ and particle number $N$ is

where $\Xi$ is the grand partition function and $\beta = 1/(k_B T)$.

Applications

• Open systems in chemistry and biology.
• Quantum gases with variable particle number.
• Adsorption phenomena.