Edit: @Dale managed to do a far better job in stating the problem, essentially the question is why do we get the same internal energy for different microstates corresponding to a single thermodynamic state Original Post: So I'm self studying a course about thermodynamics and statistical physics ( due to personal issues I could not attend the lectures ) using Mehran Kardar's Statistical Physics of Particles, the book starts with thermodynamics, it started with the zeroth law which after some struggle I think I've got a grip on. Now I'm tackling the first law and and I just cannot understand the reasoning behind it, it states that the work required to change an adiabatically insulated system from one state to another is a function of only the initial and final states, in other words it implies the existence of and energy function for the states, which is called the internal energy. After some digging around the internet I saw that it was stated in multiple places that the internal energy is a measure of the energy of the constitute particles (kinetic, potential, bond, etc..), this explains the conservation of energy ( because essentially when talking about heat transfer we're talking about the mechanical transfer of energy at the microscopic level), what it doesn't explain is how come that the internal energy can be a function of state seeing that there are multiple microscopic configurations to produce the same state, that implies that every single configuration has the same energy which I doubt is true. I guess my question is can anyone explain internal energy to me? because the way I understand it, it should not exist in the first place.