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Quantum mechanics, the cornerstone of modern physics, provides a fundamental framework for describing the behaviour of particles at the microscopic scale. It departs from classical physics by introducing the concept of quantization, where energy and other properties of particles can only take on certain discrete values.

Fermi energy is an essential concept arising from this quantum terrain and pertains to the behavior of electrons, which are fermions — particles that follow Pauli's exclusion principle. This principle states that no two fermions can occupy the same quantum state simultaneously. In a solid material, electrons fill available energy states from the lowest up until all are occupied, leading to a 'Fermi sea' of electron states. The Fermi energy marks the top of this sea at absolute zero temperature.

The relationship between Fermi energy and volume in a quantum gas makes more sense when viewed through a quantum mechanics lens. As volume changes, so does the quantization of energy levels. More volume means more space for energy levels, leading to a decrease in energy differences between levels and thereby a lower Fermi energy.

A quantum gas is a collection of particles that abide by the rules of quantum statistics. Fermions and bosons represent the two categories of particles, which behave according to Fermi-Dirac and Bose-Einstein statistics, respectively.

In the context of a fermionic quantum gas, like an electron gas in a metal, the effects of quantum statistics are profound at very low temperatures. This encompasses scenarios close to absolute zero, where the Fermi-Dirac distribution comes into play. Under such conditions, the behavior of particles differs greatly from classical ideal gases. The quantization of energy levels means that the electrons will fill these levels in a way that is distinct from classical particles, which is why squeezing more 'quantum' electrons into the same volume increases the Fermi energy.

The quantum description is necessary to accurately explain the properties of these gases, as classical mechanics cannot account for the discrete occupation of energy levels by electrons, a characteristic trait that profoundly influences electric and thermal properties of materials.

Absolute zero, a theoretical state, is the lowest temperature possible, where a system reaches its minimum possible energy, known as the ground state in quantum mechanics. It is defined as 0 Kelvin (-273.15°C or -459.67°F).

At absolute zero, all classical motion of particles ceases, and particles settle into their lowest energy states due to quantum rules. For a fermionic system, this implies that the particles fill up the lowest available energy states up to the Fermi energy. Beyond this, there are no more filled states at absolute zero. While it's impossible to reach this temperature due to the Third Law of Thermodynamics, it provides a useful theoretical point to understand the distribution of particle energies in a quantum gas.

Therefore, when we consider the Fermi energy in relation to volume, the concept of absolute zero temperature helps us to understand how a quantum gas would behave under idealized conditions. With no thermal energy to excite particles to higher states, the Fermi energy becomes the ceiling for electron energies within a material at this lower bound of temperature.