# Does the basic postulate about equilibrium violate the minimum energy principle?

For the sake of simplicity, suppose that the volume V of the system is its only relevant external parameter. An isolated system of this kind consists then of a given number N of particles in a specified volume V, the constant energy of the system being known to lie in some range between E and E + delta E. Probability statements are then made with reference to an ensemble which consists of many such systems, all consisting of this number N of particles in this volume V, and all with their energy lying in the range between E and E + delta E. The fundamental statistical postulate asserts that in an equilibrium situation the system is equally likely to be found in any one of its accessible states.

My qustion is whether this fundamental statistical postulate violate the minimum energy principle for it assumes that the higher energy case will be equally likely to occur as the lower energy case.

The term accessible is important. The states that are accessible by the system are the ones that have the macroscopic variables fixed to the values taken at equilibrium. This includes energy. So what this says is that all the states who have volume $$V$$, number if particles $$N$$ and energy $$E$$ are equally likely.
• Yes. But $\Delta E\to 0$ – Superfast Jellyfish Mar 1 '20 at 5:42