Thermodynamics

Thermodynamics typically deals with systems in equilibrium states that do not change over time under steady conditions. However, real processes like heating or compression occur over time. This apparent contradiction is resolved by introducing

quasi-static processes^[1], which evolve so gradually that the system stays nearly in equilibrium throughout. The system's macroscopic variables such as pressure and volume can then be plotted continuously in what's known as state space or configuration space.

If external conditions change too quickly, the system may deviate from equilibrium, making variables like pressure and temperature undefined. For example, a rapid gas compression can generate shock waves that cause non-uniformities, resulting in a process that cannot be represented as a continuous line between equilibrium states.

Reversible processes are idealized, quasi-static paths that can proceed in either direction without any net change in the system or surroundings. Most quasi-static processes are reversible, but some exceptions exist, like the slow stirring of a fluid, which produces irreversible internal heating. Still, if the energy added by stirring is removed via thermal exchange with a bath, the system can be brought back along the same path in reverse, effectively inverting the process in the configurational space.