Thermodynamics/Notes

Fundamental entities in thermodyanics or thermal physics:

entropy
 * Measures the number of quauntum states accessible to a closed system. The logical assumption is made that a system state is either accessible or not accessible.  The system is assumed to have equal probability of being in any accessible state.

Given g accessible states the entropy is defined as: sigma=log g
 * Thus entropy is a function of system energy U, system components or particles N, and the volume V of the system ..... because these three parameters effect g, the number of accessible system states. sigma=log(g(U,N,V))  by definition.  Logs are used for math convenience.

Two systems brought into contact can transfer energy back and forth thus increasing the number of possible states accessible to new total system. (g1g2) > (g1 + g2) by asumption and later empirical proof. This is key to 2nd law thermodynamics and law of of entropy always increases. Energy does not flow in ways to decrease the number of possible states accessible to the closed system or the entropy always increases.
 * Consider a cooling solution, entropy is decreasing as rock salt solution crystallizes for the solid salt crystal .... but it is not a closed system. Heat is transferring to ambient environment.  Total entropy  sigma(salt)+sigma(rest of universe)=sigma(universe total) of the perceived universe must be rising or there would be no energy flow.
 * This is a fundamental assumption defining energy flow and no credible evidence contradicting it has ever been reliably and reproducibly observed and reported.

Temperatures
Boltzmann Constant

chemical potential

Gibbs factor

distribution functions

closed system - A system enclosed by a control surface across which nothing relevant to the defined system crosses.