We study the relaxation of a quantum system towards the thermal equilibrium using tools developed within the context of quantum information theory. We consider a model in which the system is a qubit, and reaches equilibrium after several successive two-qubit interactions (thermalizing machines) with qubits of a reservoir. We characterize completely the family of thermalizing machines. The model shows a tight link between dissipation, fluctuations, and the maximal entanglement that can be generated by the machines. The interplay of quantum and classical information processes that give rise to practical irreversibility is discussed.We study the relaxation of a quantum system towards the thermal equilibrium using tools developed within the context of quantum information theory. We consider a model in which the system is a qubit, and reaches equilibrium after several successive two-qubit interactions (thermalizing machines) with qubits of a reservoir. We characterize completely the family of thermalizing machines. The model shows a tight link between dissipation, fluctuations, and the maximal entanglement that can be generated by the machines. The interplay of quantum and classical information processes that give rise to practical irreversibility is discussed.

arXiv:quant-ph/0110088Physical Review LettersFeb 19, 2002312 citations

Entanglement theory and the second law of thermodynamics

Fernando G. S. L. Brandão, Martin Bodo Plenio

arXiv:0810.2319Nature PhysicsOct 12, 2008189 citations

Thermalization and irreversibility of an isolated quantum system II

Guo, Xue-Yi

The irreversible entropy increase described by the second law of thermodynamics is fundamentally tied to thermalization and the emergence of equilibrium. In the first part of our work (Ref: arXiv.2503.04152), we constructed an isolated gas system model and numerically demonstrated irreversible growth of entanglement entropy caused by erasure of spread non-equilibrium state information. Here, we mathematically prove that for a typical macroscopic system in a non-equilibrium state $|ϕ_0\rangle$ , the quantum state $|ϕ'_0\rangle = \hat{O}(t)|ϕ_0\rangle$ will inevitably evolve toward equilibrium. Our work demonstrates that the second law of thermodynamics, and consequently the ergodic hypothesis in statistical physics, can be understood and proven from a quantum information perspective. From this perspective, the second law can be stated as: In typical macroscopic physical systems, the spreading and erasure of non-equilibrium information is inevitable.The irreversible entropy increase described by the second law of thermodynamics is fundamentally tied to thermalization and the emergence of equilibrium. In the first part of our work (Ref: arXiv.2503.04152), we constructed an isolated gas system model and numerically demonstrated irreversible growth of entanglement entropy caused by erasure of spread non-equilibrium state information. Here, we mathematically prove that for a typical macroscopic system in a non-equilibrium state $|ϕ_0\rangle$, the quantum state $|ϕ'_0\rangle = \hat{O}(t)|ϕ_0\rangle$ will inevitably evolve toward equilibrium. Our work demonstrates that the second law of thermodynamics, and consequently the ergodic hypothesis in statistical physics, can be understood and proven from a quantum information perspective. From this perspective, the second law can be stated as: In typical macroscopic physical systems, the spreading and erasure of non-equilibrium information is inevitable.

arXiv:2506.01351Jun 2, 20250 citations

Equilibrium State and Entanglement

Sho Sugiura

Springer thesesJan 1, 20170 citations

Thermalization and irreversibility of an isolated quantum system

Xueyi Guo

The irreversibility and thermalization of many-body systems can be attributed to the erasure of spread non-equilibrium state information by local operations. This thermalization mechanism can be demonstrated by the sequence of $\hat{O}_i(t_i)$ , where $\hat{O_i}$ is a local operator, $\hat{O_i}(t_i) = e^{i\hat{H}t_i} \hat{O_i} e^{-i\hat{H}t_i}$ , $\hat{H}$ is the system Hamiltonian, $t_i$ can take positive, negative, or zero values, and the sequence is arranged according to the subscript $i$ . We numerically demonstrate the information erasure of initial non-equilibrium quantum states through such sequence in a one-dimensional Hubbard model. During this process, the system's entanglement entropy increases monotonically toward a stable value. By incorporating this information erasure mechanism into an isolated system, our numerical simulations reveal that in this completely isolated system, a thermalization process emerges.The irreversibility and thermalization of many-body systems can be attributed to the erasure of spread non-equilibrium state information by local operations. This thermalization mechanism can be demonstrated by the sequence of $\hat{O}_i(t_i)$, where $\hat{O_i}$ is a local operator, $\hat{O_i}(t_i) = e^{i\hat{H}t_i} \hat{O_i} e^{-i\hat{H}t_i}$, $\hat{H}$ is the system Hamiltonian, $t_i$ can take positive, negative, or zero values, and the sequence is arranged according to the subscript $i$. We numerically demonstrate the information erasure of initial non-equilibrium quantum states through such sequence in a one-dimensional Hubbard model. During this process, the system's entanglement entropy increases monotonically toward a stable value. By incorporating this information erasure mechanism into an isolated system, our numerical simulations reveal that in this completely isolated system, a thermalization process emerges.

arXiv:2503.04152Mar 6, 20250 citations

|ϕ_0\rangle

, the quantum state

|ϕ'_0\rangle = \hat{O}(t)|ϕ_0\rangle

will inevitably evolve toward equilibrium. Our work demonstrates that the second law of thermodynamics, and consequently the ergodic hypothesis in statistical physics, can be understood and proven from a quantum information perspective. From this perspective, the second law can be stated as: In typical macroscopic physical systems, the spreading and erasure of non-equilibrium information is inevitable.

\hat{O}_i(t_i)

, where

\hat{O_i}

is a local operator,

\hat{O_i}(t_i) = e^{i\hat{H}t_i} \hat{O_i} e^{-i\hat{H}t_i}

\hat{H}

is the system Hamiltonian,

t_i

can take positive, negative, or zero values, and the sequence is arranged according to the subscript

i

. We numerically demonstrate the information erasure of initial non-equilibrium quantum states through such sequence in a one-dimensional Hubbard model. During this process, the system's entanglement entropy increases monotonically toward a stable value. By incorporating this information erasure mechanism into an isolated system, our numerical simulations reveal that in this completely isolated system, a thermalization process emerges.