Quantum thermodynamics is a framework that combines the principles of quantum mechanics and thermodynamics. It extends classical thermodynamics to the quantum realm, where systems are described by quantum states and operators.

Quantum temperature is a measure of the average energy of a quantum system. It is defined as the expectation value of the Hamiltonian operator divided by the Boltzmann constant.

Black holes are predicted to have negative absolute temperature. This is because the Hawking radiation emitted by black holes has a thermal spectrum with a negative temperature.

Quantum heat engines, quantum refrigerators, and quantum Carnot cycles are all quantum analogs of their classical counterparts. They operate on the principles of quantum mechanics and can achieve higher efficiencies than classical devices.

Laser cooling is a technique that uses the absorption and re-emission of photons to cool atoms and molecules to ultra-low temperatures. It works by selectively exciting and de-exciting atoms or molecules with laser light.

The Fermi-Dirac distribution describes the statistical distribution of fermions, which are particles that obey the Pauli exclusion principle. It is used to calculate the energy levels and occupation probabilities of fermions in quantum systems.

Wave-particle duality is the fundamental property of matter that it can exhibit both wave-like and particle-like behavior. In the context of quantum thermodynamics, wave-particle duality leads to the quantization of energy levels in atoms and molecules.

Von Neumann entropy, Rényi entropy, and Tsallis entropy are all quantum analogs of classical entropy. They are used to quantify the uncertainty or disorder in quantum systems.

Quantum tunneling is a quantum phenomenon that allows particles to pass through potential barriers even if they do not have enough energy to do so classically. It plays a crucial role in many quantum processes, such as nuclear fusion and scanning tunneling microscopy.

Quantum work is the quantum analog of classical work. It is defined as the expectation value of the change in the Hamiltonian operator of a quantum system.

Spontaneous emission is a quantum phenomenon in which an atom or molecule in an excited state spontaneously emits a photon and transitions to a lower energy state. It is the fundamental process behind the emission of light by lasers and other optical devices.

Quantum heat capacity is the quantum analog of classical heat capacity. It is defined as the amount of heat required to raise the temperature of a quantum system by one unit.

Quantum entanglement is a quantum phenomenon in which two or more particles become correlated in such a way that the state of one particle cannot be described independently of the other, even when they are separated by a large distance.

Quantum power is the quantum analog of classical power. It is defined as the rate at which work is done on or by a quantum system.

Wave-particle duality is the fundamental property of matter that it can exhibit both wave-like and particle-like behavior. In the context of quantum thermodynamics, wave-particle duality leads to the quantization of angular momentum.