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I am currently working through a book about thermodynamics and statistical mechanics as I was not so great in these course during my undergrad studies.

**First question:**The book introduces heat as the kind of energy that terminates the temperature of a system. In other words: Give heat to a system, the temperature will increase. A system with higher temperature holds more heat.

The difference between temperature and other energy (the author calls it "work", so the energy that can be extracted as physical work) can be understood microscopically. Heat is energy that is statistically distributed over all particles, whereas work is other energy, e.g stored in directed motions of particles. E.g. if all particles flow in the same direction, this flow can be used as work.

From the equipartition theorem we know that the average kinetic energy is proportional to the temperature.

From that point of view, if we had N particles flowing in the same direction the temperature of the system would increase with flow velocity. Meaning the heat in the system would,

**in contrast**to what the author claimed, be stored in more and more directed motion.

I went back to check the conditions under which the equipartition theorem holds: He says, it holds in thermodynamic equilibrium. However, in the very beginning of the book, he uses "thermodynamic equilibrium" and "thermal equilibrium" interchangeably as a state where T=const over the whole system (or between different systems when they are in equilibrium with each other).

That would imply that a flowing system with uniform temperature T was in thermal/thermodynamic equilibrium and the equipartition theorem would hold which would lead to the strange conclusion that higher flow velocity => higher T (and to the fact that his microscopical explanation of heat was wrong).

Google shows thermal equilibrium is just PART of thermodynamic equilibrium. In the latter, there has to be chemical and mechanical equilibrium as well. Is a flowing system in mechanical equilibrium? Probably not, because if I were to put a wall in the flow, there would be a force on this wall. So the flowing system is not in thermodynamic equilibrium. If the equipartition theorem was legit only in thermodynamic equilibrium, then everything would be fine (the author simply should have stressed the difference between the two equilibrium terms). But on Wiki(https://en.wikipedia.org/wiki/Equipartition_theorem), it says that the equipartition theorem holds for

**thermal**equilibrium, not thermodynamic equilibrium.

So is Wiki wrong and the equipartition theorem holds only for thermodynamic equilibrium?

Or is the explanation of heat wrong in my book?

Thanks for following my thoughts^^