Photon gas

A photon gas is a unique collection of light particles known as photons. While we often think of light as waves, these particles behave like a gas in many ways. They possess properties like temperature, pressure, and entropy, much like a conventional gas of hydrogen or neon. However, photons belong to a specific family of particles called bosons. Bosons are particles that follow Bose-Einstein statistics and possess an integer spin. Because of these quantum properties, a photon gas behaves quite differently from the massive particles found in everyday air.

In a standard ideal gas, particles have mass and frequently collide with one another. These collisions allow the particles to exchange energy and momentum, creating an equilibrium distribution called a Maxwell-Boltzmann distribution. A photon gas is different because photons generally do not collide with each other. Instead, the equilibrium distribution is established through interactions with matter. In a common example, such as black-body radiation, the photons interact with the walls of their container. These walls absorb and emit photons, which sets the energy distribution for the entire gas.

One of the most significant differences between a photon gas and a gas of massive bosons is particle conservation. In a normal gas, the number of particles stays the same unless you add or remove them. In a black-body photon gas, the number of photons is not conserved. Photons can be created through a process called thermal emission. This happens when an atom in a wall is thermally excited into an upper electronic state and then falls back to a lower state. This movement releases a new photon into the gas. Conversely, a photon can be destroyed when it is absorbed by an atom. Because the number of photons can change freely, the chemical potential of a black-body photon gas is zero.

This lack of particle conservation changes how scientists describe the system. For a generic Bose gas, you need three state functions: temperature, volume, and the number of particles. For a black-body photon gas, the number of variables is reduced to two, such as temperature and volume. This is because the photon number adjusts itself to maintain a constant density for a given temperature. The energy distribution of these photons is described by Planck's law. This law calculates the spectral energy density, which is the energy per unit volume per unit frequency interval. It uses several constants, including the Planck constant, the speed of light, the Boltzmann constant, and the temperature.

We can use complex mathematics to find the total internal energy of this gas. By integrating Planck's law over all frequencies and multiplying by the volume, we find the total energy. The expected number of photons also follows a specific mathematical relationship involving the Riemann zeta function. For an ultra-relativistic quantum gas, which describes photons, the equation of state relates pressure and energy density. Specifically, the pressure is equal to one-third of the energy density. This relationship shows that the pressure of a photon gas is independent of its volume. This is a fundamental characteristic of how light exerts radiation pressure.

To visualize these forces, imagine a cylinder containing a photon gas with a movable piston. The interior walls of this cylinder are "black" to maintain a steady temperature. If you push the piston inward to decrease the volume, the photon gas will press against it. To move the piston very slowly and keep the process isothermal, you must apply a counter force. This force is equal to the pressure multiplied by the cross-sectional area of the piston. This experiment demonstrates how the energy required to create the gas is related to its enthalpy. The enthalpy represents the total amount of energy needed to establish the photon gas at a certain volume.

Modern physics also explores ways to create photon gases with a tunable chemical potential. This is achieved in low-dimensional systems, such as optical microcavities filled with dye solutions. In these tiny environments, the distance between resonator mirrors is within the wavelength range, making the system behave in two dimensions. When the chemical potential can be controlled, the photon gas begins to behave much more like a gas of material particles. Under these high phase space densities, a remarkable phenomenon called Bose-Einstein condensation can occur. This allows light to reach a state of matter previously associated only with massive particles.