- #1
nonequilibrium
- 1,439
- 2
Hello,
I was investigating a system with N indistinguishable particles, each of which can have an energy [itex]\pm \epsilon[/itex], and using the grand canonical ensemble, i.e. [itex]\Xi = \sum_{N=0}^{\infty} e^{\beta \mu N} Z_N[/itex].
But my entropy formula is [itex]S = \left( \textrm{a couple of $\sim N $ positive terms } \right) - N \ln N[/itex]. Not only is this formula not extensive, it also indicates that the entropy will get (arbitrarily) negative for large N! (Also, the formula depends on the temperature, but I'm keeping that constant.)
Note: to avoid confusion, the N that appears in the formula is actually [itex]\langle N \rangle [/itex].
Must this be a calculation error? The calculation is not long and I've looked through it carefully and everything is straight-forward... I'm quite confused at this point!
I was investigating a system with N indistinguishable particles, each of which can have an energy [itex]\pm \epsilon[/itex], and using the grand canonical ensemble, i.e. [itex]\Xi = \sum_{N=0}^{\infty} e^{\beta \mu N} Z_N[/itex].
But my entropy formula is [itex]S = \left( \textrm{a couple of $\sim N $ positive terms } \right) - N \ln N[/itex]. Not only is this formula not extensive, it also indicates that the entropy will get (arbitrarily) negative for large N! (Also, the formula depends on the temperature, but I'm keeping that constant.)
Note: to avoid confusion, the N that appears in the formula is actually [itex]\langle N \rangle [/itex].
Must this be a calculation error? The calculation is not long and I've looked through it carefully and everything is straight-forward... I'm quite confused at this point!