# Statistical mechanics with a negative amount of atoms

by Catria
Tags: atoms, mechanics, negative, statistical
 P: 56 My advanced statistical mechanics prof told me that it wouldn't make any physical sense to allow N (the number of particles in a system) to be negative. But, somehow, I think that this possibility should be theoretically left open; perhaps there are some systems whose statistical behavior would be best explained if we allowed N < 0. My question is: what would happen if we wanted to solve stat-mech problems of systems with negative quantities of particles?
 P: 3,014 Do you know why thermodynamic temperature must be a positive quantity?
P: 56
 Quote by Dickfore Do you know why thermodynamic temperature must be a positive quantity?
Is it possible to have a thermodynamic themperature > 0 with N < 0?

 Emeritus Sci Advisor PF Gold P: 16,459 Statistical mechanics with a negative amount of atoms Your professor is right. What does it even mean to say "I have negative four atoms in this box"? Sure, you can always plug numbers into equations, but that doesn't mean what comes out makes any sense.
 P: 56 Come to think of it, a system whose statistical behavior is that of N < 0 would be quantum in nature, regardless of whether the system contains bosons or fermions.
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P: 1,391
 Quote by Catria My advanced statistical mechanics prof told me that it wouldn't make any physical sense to allow N (the number of particles in a system) to be negative. But, somehow, I think that this possibility should be theoretically left open; perhaps there are some systems whose statistical behavior would be best explained if we allowed N < 0. My question is: what would happen if we wanted to solve stat-mech problems of systems with negative quantities of particles?
Which systems' statistical behavior do you think would be best explained if we allowed N < 0? Do you have any examples in mind?

I doubt there's any physical meaning to having a negative number of particles, even in quantum statistical mechanics. Even in ensembles in which you allow particle fluctuations, they don't have fluctuations to less than zero particles in the system.

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