# What really is a thermodynamic system?

I'm starting to study Thermodynamics and I'm pretty confused about what a thermodynamic system really is. When studying mechanics we focus our attention on systems of particles. So when we talk about systems of particles we know what is it all about, a collection of some particles in space subject (or not) to a collection of constraints.

When we study fluids, for example, the fluid is still a system of particles, each particle being a molecule of the fluid. But now this description is too messy to work with, so we use the continuum approximation. Anyway, again we have a system of particles in some region in space.

Now, in Thermodynamics, what is a thermodynamic system? Texts usually talk about "pressure" and "volume" like if it were a fluid, but certainly Thermodynamics is much more general than just fluids. Wikipedia's page says the following:

A thermodynamic system is a macroscopic volume in space, the adventures of which are to be studied according to the principles of thermodynamics, along with its walls and surroundings. Not just any physical system is a thermodynamic system, but only those that can be adequately described by thermodynamic variables, such as temperature, entropy, internal energy, and pressure.

So a thermodynamic system is just a system of lots of molecules of some substance with the continuum assumptions we make in fluid mechanics? What really is the definition of a thermodynamic system and what's the motivation behind the definition?

– BMS
Sep 9, 2014 at 20:49
• A thermodynamic system is one that satisfies the near equilibrium conditions of thermodynamics. It can be a single particle or a universe full of galaxies, as long as one can define suitable thermodynamic variables, it's all good. This, by the way, is no different from the definitions of "Newtonian system" or "quantum mechanical system", just the criteria which these systems have to fulfill differ. Sep 9, 2014 at 20:56
• @CuriousOne I'm not sure I agree. I've almost exclusively encountered the term applied to systems in the thermodynamic limit which necessitates a large number of particles. Sep 9, 2014 at 21:46
• @joshphysics: If you look at the formula for entropy in statistical mechanics, all it requires is a summation over all the micro states of a system. Those states can be the states of one atom or the (standing) electromagnetic waves in a cavity. The lowest possible number of states can even be two: spin up and spin down for a single spin 1/2 particle. If you couple that kind of system to a (classical!) temperature bath, the formalism will still deliver very valid and very useful results. To me that qualifies as a thermodynamic system. You are correct that most applications have large N, though. Sep 9, 2014 at 21:52
• @CuriousOne I would call that "statistical mechanics" not "thermodynamics." Sep 9, 2014 at 22:01