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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?

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    $\begingroup$ Adventures of the macroscopic volume sounds like an interesting read. $\endgroup$ – BMS Sep 9 '14 at 20:49
  • $\begingroup$ 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. $\endgroup$ – CuriousOne Sep 9 '14 at 20:56
  • $\begingroup$ @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. $\endgroup$ – joshphysics Sep 9 '14 at 21:46
  • $\begingroup$ @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. $\endgroup$ – CuriousOne Sep 9 '14 at 21:52
  • $\begingroup$ @CuriousOne I would call that "statistical mechanics" not "thermodynamics." $\endgroup$ – joshphysics Sep 9 '14 at 22:01
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Wikipedia is talking *&^%)+#.

The laws of thermodynamics apply to everything, so everything is a thermodynamic system. Equilibrium thermodynamics, commonly studied at an elementary level, is the study of materials which are either in equilibrium, or undergoing changes so slow that they can be considered to be passing through a series of equilibria. These have a well-defined temperature, uniform and isotropic pressure, and so on. Even here, however, you do not have to make the continuum assumption - the study of thermodynamics from an atomistic (or quantum) point of view is known as statistical mechanics.

Thermodynamics itself, however, includes the study of systems far from equilibrium. Admittedly, in these situations it has less predictive power.

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  • $\begingroup$ Hmm. I'm not sure I agree that "everything is a thermodynamic system." In my experience, most physicists reserve that term for a system in the thermodynamic limit, namely the limit in which there (at least) is a large number of particles in the system. $\endgroup$ – joshphysics Sep 9 '14 at 21:42
  • $\begingroup$ Thermodynamics has zero predictive power for the Kepler problem, chaos, turbulence or the Schroedinger solution of the hydrogen atom. Indeed, if you were to couple a temperature bath to either of these, it would strongly distort, if not destroy the solution space of either problem. It is not customary to call these "thermodynamic systems". $\endgroup$ – CuriousOne Sep 9 '14 at 21:56

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