To understand entropy we must first distinguish two levels of description of the same physical system. On one hand there is what we can actually observe and measure; on the other, everything that happens at the level of individual particles, which remains hidden from us.
Principle — Macrostate vs microstate
The macrostate of a system is described by the few observable macroscopic quantities: for a gas . The microstate is the complete description of every particle (position and velocity of each one). A single macrostate generally corresponds to very many microstates.
The intuition is this: knowing the macrostate means having partial knowledge of the system, while knowing the microstate would mean having total knowledge. When we measure the pressure, volume and temperature of a gas, we really know very little about what each of the roughly molecules is doing: we only know that, taken together, they produce those average values. There are an enormous number of different microscopic configurations — molecules arranged and moving in different ways — that would all give exactly the same .
The number of microstates compatible with a given macrostate is called (omega). It is the central quantity of the whole chapter. If is large, the number of ways the system can realise that macrostate is huge, and so our ignorance about which is the true microstate is large. If were small — in the limit , a single possible microstate — we would know exactly the state of every particle.
It is precisely this idea, “many microstates much ignorance much entropy”, that the next note will turn into a precise formula and connect, surprisingly, to the concept of information.
Links
Topics: Entropy and the second law Concepts: Entropy Skills: Micro-macro interpretation Objects: Ideal gas
Related exercises: Worked exercise — the coffee cools down · Hot shower: ΔS of the universe · Heat from hot to cold: proof