2009/10/31 by J. M. Deutsch · 6 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Eigenvalues and eigenvectors #Entropy (arrow of time) #Physics #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Statistical physics #Theoretical physics #Thermodynamics #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1088/1367-2630/12/7/075021
18 pages
arxiv created 2009/10/31 · openalex publication_date 2010/07/26 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It is argued that a typical many-body energy eigenstate has a well-defined thermodynamic entropy and that individual eigenstates possess thermodynamic characteristics analogous to those of generic isolated systems. We examine large systems with eigenstate energies equivalent to finite temperatures. When quasi-static evolution of a system is adiabatic (in the quantum mechanical sense), two coupled subsystems can transfer heat from one subsystem to another and yet remain in an energy eigenstate. To explicitly construct the entropy from the wave function, degrees of freedom are divided into two unequal parts. It is argued that the entanglement entropy between these two subsystems is the thermodynamic entropy per degree of freedom for the smaller subsystem. This is done by tracing over the larger subsystem to obtain a density matrix and calculating the diagonal and off-diagonal contributions to the entanglement entropy.