I'm confused about the meaning of the concept of external parameter in Statistical Mechanics. According to my textbook, the Hamiltonian of a system is a function that depends on the generalized coordinates $\{q_i\}$, the generalized moments $\{p_i\}$ and the external parameters $\{X_\alpha\}$,

$$H=H \big(\{q_i\}, \{p_i\}, \{X_\alpha\}\big)$$

These external parameters are related to the generalized forces $\{Y_\alpha\}$, and the thermodynamical work can be expressed through them as

$$\delta W=\overline{\space Y}_{\alpha} d X_{\alpha}$$

What would be the physical meaning of this external parameter (and, by the way, of the generalized forces) in the context of Mechanical Statistics?



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