Thermodynamics

Isothermal Process

Isobaric Process

Adiabatic Process

Isochoric Process

Isentropic

Macrostate

Defined by large-scale, measurable thermodynamic variables: Temperature (T), Pressure (P), Volume (V), and Internal Energy (U)

Microstate

Defined by specifying the exact quantum state or classical phase space coordinates—positions (r1,….rn) and momenta (p1,….pn)—of every single particle.

Ergodicity

An ergodic system is one where a single trajectory in phase space will eventually explore all possible microstates that have the same total energy E. Inter-particle collisions break $3N$ individual momentum constraints so the system explores all microstates of fixed total energy E.

Extensive vs Intensive Variables

Extensive Variables (S, V, N, E, U): Scale linearly with system size. If you double the system size (lambda = 2), the value doubles

Intensive Variables (T, P, mu): Do not depend on system size. If you double the system size, the value stays exactly the same.

Equipartition Theorem

The equipartition theorem states that in thermal equilibrium, every degree of freedom that appears quadratically in a system's total energy possesses an average energy of ½ KbT

Diffusion Coefficient

The diffusion coefficient D measures how fast a random process spreads out in space per unit time.