Thermodynamic equilibrium

Thermodynamic equilibrium is a fundamental concept in the study of thermodynamics. It describes a state where a single system or multiple connected systems reach a perfect balance. In this state, there are no net macroscopic flows of mass or energy. This means that on a large scale, nothing is moving from one place to another. The system shows an absence of any tendency toward change. It remains steady and unchanging unless an outside force disturbs it. This concept is an axiom, meaning it is a starting rule for the entire science.

To understand how this balance works, we must look at the microscopic level. While nothing changes on a large scale, tiny exchanges are still happening. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur. This is the physical explanation for why the system appears still. If a system is not in equilibrium, there are net flows of matter or energy. If a system is stable but could be triggered to change, it is called a meta-stable equilibrium. This shows that equilibrium is a specific point of stability.

There are several distinct types of equilibrium that must happen at once for true thermodynamic equilibrium. First, there is thermal equilibrium, which occurs when two systems have the same temperature. Second, mechanical equilibrium happens when the pressures of the systems are the same. Third, diffusive equilibrium occurs when the chemical potentials are equal. Finally, radiative equilibrium exists when systems reach the same temperature through radiation. A system can be in one kind of equilibrium without being in the others. However, true thermodynamic equilibrium requires all these types to hold indefinitely.

Scientists use specific mathematical tools to identify these states. For a completely isolated system, the entropy, or the measure of disorder, is at its maximum. For a closed system kept at a constant temperature and volume, we look at the Helmholtz free energy, denoted as A. At equilibrium, this value is at its minimum. If the system is at constant temperature and pressure, we use the Gibbs free energy, denoted as G. This value must also be minimized. These potentials are mathematical ways to find the unique stable state of a system.

History shows how these rules were developed through observation. The second law of thermodynamics is a key rule in this field. It states that in an isolated system, if you remove partitions between different subsystems, the system will spontaneously equilibrate. This process is accompanied by an increase in entropy. In 1914, Max Planck described radiative exchange equilibrium. He noted that it prevails when two systems share the same temperature. These discoveries helped define how energy moves and settles in the universe.

We can observe these principles in various settings. In a system with a vertical gravitational field, the pressure might change from top to bottom. However, the temperature remains spatially uniform. This shows that temperature is a unique intensive variable that stays the same everywhere in equilibrium. Another example is contact equilibrium. This occurs when two systems touch through a boundary with specific permeability. If a wall only allows heat to pass, the systems reach thermal equilibrium when heat transfer stops. If a wall allows work, they reach mechanical equilibrium.

Thermodynamics also distinguishes between global and local equilibrium. Global thermodynamic equilibrium means that intensive parameters are the same throughout the entire system. Local thermodynamic equilibrium is a different state. In this case, parameters may vary in space and time, but they change so slowly that they can still be treated as being in equilibrium locally. Understanding these differences helps scientists study complex, moving systems. It allows them to predict how a system will eventually settle into its final, stable state after a natural thermodynamic process occurs.