Speaker
Description
The second law of thermodynamics for adiabatic operations --- constraints on state transitions in closed systems under external control --- is one of the fundamental principles of thermodynamics. On the other hand, recent studies of thermalization have established that even pure quantum states can represent thermal equilibrium. However, pure quantum states do not satisfy the second law in that they are not passive, i.e., work can be extracted from them if arbitrary unitary operations are allowed, and that various entropy formulas, such as the von Neumann entropy, deviate from thermodynamic entropy in such states. It therefore remains unresolved how thermal equilibrium represented by a pure quantum state can be reconciled with thermodynamics. Here, based on our key quantum-mechanical notions of thermal equilibrium and adiabatic operations, we address the emergence of the second law of thermodynamics in closed quantum many-body systems. We first introduce infinite-observable macroscopic thermal equilibrium (iMATE); a quantum state, including pure states, is said to represent iMATE if the expectation values of all additive observables, which correspond to additive quantities in thermodynamics, agree with their equilibrium values. We also introduce a macroscopic operation as unitary evolution generated by a time-dependent additive Hamiltonian, which is regarded as corresponding to adiabatic operations. Employing these concepts, we show Planck's principle: no extensive work can be extracted from any quantum state representing iMATE through any macroscopic operations with the operation times independent of the system size. Furthermore, we introduce a quantum-mechanical form of entropy density such that it agrees with thermodynamic entropy density for any quantum state representing iMATE. We then prove the law of increasing entropy: for any initial state representing iMATE, this entropy density cannot be decreased by any macroscopic operations with the operation times independent of the system size, followed by a relaxation process governed by a time-independent Hamiltonian. Our theory thus proves two different forms of the second law, which are quantum mechanically inequivalent to each other, and demonstrates how thermodynamics emerges from quantum mechanics by adopting macroscopically reasonable classes of observables, equilibrium states, and operations. This presentation is based on arXiv:2602.06657.