2015/03/27 by Shraddha Sharma, Amit Dutta
Mathematics · Physics and Astronomy · #Absolute zero #Advanced Thermodynamics and Statistical Mechanics #Configuration entropy #Entropy (arrow of time) #Ground state #Hamiltonian (control theory) #Logarithm #Mathematical analysis #Mathematics #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Quantum thermodynamics #Residual entropy #Scaling #Scaling limit #Statistical physics #Thermodynamic limit #Thermodynamics #Topological Materials and Phenomena #Work (physics) #Zero temperature #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.92.022108
7 pages, 6 figures
arxiv created 2015/03/27 · openalex publication_date 2015/08/06 · arxiv updated 2015/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Using the scaling relation of the ground state quantum fidelity, we propose the most generic scaling relations of the irreversible work (the residual energy) of a closed quantum system at absolute zero temperature when one of the parameters of its Hamiltonian is suddenly changed. We consider two extreme limits: the heat susceptibility limit and the thermodynamic limit. It is argued that the irreversible entropy generated for a thermal quench at low enough temperatures when the system is initially in a Gibbs state is likely to show a similar scaling behavior. To illustrate this proposition, we consider zero-temperature and thermal quenches in one-dimensional (1D) and 2D Dirac Hamiltonians where the exact estimation of the irreversible work and the irreversible entropy is possible. Exploiting these exact results, we then establish the following. (i) The irreversible work at zero temperature shows an appropriate scaling in the thermodynamic limit. (ii) The scaling of the irreversible work in the 1D Dirac model at zero temperature shows logarithmic corrections to the scaling, which is a signature of a marginal situation. (iii) Remarkably, the logarithmic corrections do indeed appear in the scaling of the entropy generated if the temperature is low enough while they disappear for high temperatures. For the 2D model, no such logarithmic correction is found to appear.