# Thermodynamics (Enrico Fermi): Thermodynamic vs. Dynamical State

1. Jul 4, 2009

### juni

I'm reading Enrico Fermi's "Thermodynamics" book. In page 3 of his book, he says:

It is evident from what we have said that the knowledge of the thermodynamical state alone is by no means sufficient for the determination of the dynamical state.

What does he mean by dynamical state? What's the difference between the thermodynamic state and the dynamical state?

Studying the thermodynamical state of a homogenous fluid of given volume at a given temperature (the pressure is then defined by the equation of state), we observe that there is an infinite number of states of molecular motion that correspond to it. With increasing time, the system exists succesively in all these dynamical states that correspond to the given thermodynamical state. From this point of view, we may say that a thermodynamical state is the ensemble of all the dynamical states through which, as a result of the molecular motion, the system is rapidly passing.

Is he trying to say that there an infinite number of energy states given V, P and T?

This paragraph just threw me off. Can someone explain the point he is trying to make in simpler words?

Last edited: Jul 4, 2009
2. Jul 4, 2009

### Count Iblis

To specify the exact state a gas is in, you have to specify what each molecule is doing. If you just specify the volume, temperature and number of molecules, then that alone does not specify the exact state the gas is in.

3. Jul 6, 2009

### turin

I believe that "dynamical" implies specification of every single individual degree of freedom (e.g. the motion of molecules), whereas "thermodynamic" implies bulk properties (and is commonly restricted to equilibrium or quasiequilibrium condition, i.e. no heat flow, or at least the state changing along a well-defined curve).

It is probably confusing to say that there are an infinite number of energy states (which, to me, at least, sounds like it implies an infinite number of different energy values). Rather, I would say that there are a very large (practically infinite) number of states that are possible for a given energy.

IMO, the main point is that thermodynamics treats a very complicated physical system in comparitively extremely simple terms, but as a consequence you lose almost all of the physical information about the system.

4. Jul 12, 2009

### juni

Many thanks for your input. I get it know. I think I failed to recognize the word "ensemble", which in this case implies some type of averaging, and this of course is what thermodynamic states are all about.

5. Jul 13, 2009

### turin

Actually, ensemble does not imply averaging, it implies the opposite. You can think of a thermo state as a state that doesn't even necessarily exist, but it is the appropriately weighted average of all possible configurations. The set of all possible configurations is the ensemble. So, the ensemble is the description that takes into account all of the ignorance while at the same time keeping all of the information.