# Thrid law of thermodynamics and quantum mechanics

Third law of thermodynamics says that it is impossible to reach absolute zero temperature in finite numbers of operations. According to quantum mechanics, every system has energy levels and ground state. Is it possible according to quantum mechanics that any system would reach ground state in finite time by photon emission(s)? Does system have zero absolute entropy when it is in ground state?

• You should try to make your question understandable to the community. The current form has some ambiguity.
– Mass
Dec 29, 2023 at 2:27

Following Wikipedia

The third law of thermodynamics states that the entropy of a closed system at thermodynamic equilibrium approaches a constant value when its temperature approaches absolute zero. This constant value cannot depend on any other parameters characterizing the system, such as pressure or applied magnetic field. At absolute zero (zero kelvins) the system must be in a state with the minimum possible energy.

Adding to that, the word "Ground State" (GS) needs further clarification. Let me explain why.

A system may have more than one GS. One notable example is the antiferromagnetic Ising model on a triangular lattice. Due to geometric frustration, the GS spin configuration of that system can not satisfy antiferromagnetic spin alignments between any pair of neighboring bonds, leading to a huge amount of GS degeneracy (i.g. a single antiferromagnetic Ising triangle is sixfold degenerate).

Frustration occurs when lattices contain elementary triangles such as the triangular or Kagome lattice, and it leads to a ground state degeneracy following the inherent ambiguity of the spin configurations not being able to satisfy all of the antiferromagnetic interactions simultaneously.

Because of the ground state degeneracy, the system does not order even at absolute zero temperature and has a residual entropy at zero temperature, which for triangular Ising is given by

$$S(0) = 0.3383R$$

This means that the system is disordered at all temperatures and possesses no Curie point. Notice that the system is disordered not because any external parameters are influencing its dynamics but due to its inherent structure.

Another example is the resedual entropy of ice at absolute zero temperature, which arises due to the inability of the system to satisfy the famous ice rule.

One can argue that antiferromagnetic Ising in the triangular lattice is a classical system. What happens to the quantum case? In fact, the frustrated quantum system has a much richer structure, leading to exotic phases of quantum matters like quantum spin liquids. Frustrated quantum systems are an active area of research.