Relaxation time approximation

[scivet]

I was reading Chpater 13 in A&M solid state physics, which is about relaxation time approximation. But there is one fundamental expression I'm trying to understand.

It's the formulation of the relaxation-time approximation (Eq. 13.3).
dg = dt/$$\tau$$g⁰

But most of other textbooks including Ziman's and Kittel's ones say
dg/dt = -1/$$\tau$$ (g-g⁰) (Eq 7.17 in Ziman's priciples of the theory of solids).

Here g is non-equilibrium distribution function and g⁰ is equilibrium distribution function.

Though the expression looks different apparently, using both of expressions, the exactly same physical expressions for some physical properties such as electric current can be derived as shown in the textbooks.

It's easy to understand the expression in Ziman's and Kittel's ones but not easy to understand that in A&M.

Could anybody explain why the expression in A&M is different from other ones?

Thank you in advance.

 

[BigJDubs]

The difference between the two equations is that the one in A&M includes an additional factor of dt, while the one from Ziman and Kittel does not. This additional factor is necessary to account for the fact that the relaxation time is not constant over a period of time, but rather changes with the changing values of g and g0. By including this additional factor, the equation is able to capture the changes in the relaxation time as the system moves away from equilibrium.