Introduction to the research field, thermodynamics of quantum information.
In this article, I will talk about the interaction between the external world and quantum information, which is more general than decoherence. Have you ever heard of thermodynamics? It describes what happens to a group of atoms when they interact with each other. It has the famous three laws of thermodynamics, which explain most macroscopic systems. These are the law of conservation of thermal energy, the law of increasing entropy, and Nernst's law. The second law, the entropy-increasing law, is particularly important. It states that the overall clutter in a closed system increases irreversibly. For example, if you mix coffee and milk in a container, it will eventually become café au lait, and if there is friction in the motion of a pendulum, the mechanical energy will be converted into heat and the pendulum will stop moving. This is a general law that explains many common phenomena in reality. The third law of thermodynamics states that the entropy of a system at absolute zero is zero.
It was not until a quarter of a century ago that this was considered to be more strictly true in quantum mechanics. This was finally quantified by stochastic entropy generation and fluctuations in nonequilibrium physics. Stochastic entropy production is defined by considering a quantum system connected to a heat bath in thermal equilibrium with a specific distribution. From there, it can be shown that the ensemble average of the average entropy production will be greater than zero. This has become a widely used generalization of the second law of thermodynamics as the Jarzynski inequality. An elementary derivation of these things can be found in reference , please refer to that for more details. We used it to calculate the work production and entropy accumulation in the Girard engine, where entropy appears to decrease, and showed that the second law of thermodynamics holds.
Quantum mechanical entropy has already been calculated for a simple system, and its increase with time has been confirmed by numerical calculations . It is yet to be applied to various fields including quantum information.