On the notion of pressure in the canonical ensemble

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In a canonical ensemble, pressure is defined as the derivative of internal energy with respect to volume, even though the volume is fixed. This calculation considers infinitesimal changes in volume, allowing for a theoretical understanding of how energy responds to small volume variations. The concept of pressure remains valid as it describes the system's behavior under slight perturbations. Thus, while the volume is fixed in practical terms, the mathematical framework allows for pressure to be defined. Understanding this relationship is crucial for analyzing thermodynamic systems.
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Hi folks,

since the volume V is fixed in a canonical ensemble I'm a bit confused about the fact, that the pressure is calculated as the derivation of the internal energy U with respect to the volume V.

Sure, P = dU/dV comes from dU = dQ + dW = tdS - pdV + ... But what does it mean to derivate with respect to the volume, when the volume of the system can't be changed, since it is fixed. (by the way: when the volume is fixed, pdV= p*0 =0, so p is "undefined", since it can take any value.)

--
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The volume is not free to change by any significant amount, but we are considering the case where it is changed by an infinitesimal amount. In response, the system energy changes by an infinitesimal amount. The ratio is the pressure.
 

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