We develop a first-principles thermodynamic framework for non-Hermitian dynamics based on a post-selected version of the fluctuation theorem. This allows us to identify a quantity that remains positive throughout the non-Hermitian evolution and can be interpreted as the entropy production of the post-selected dynamics. We relate this quantity to previously proposed notions of non-Hermitian entropy and derive an associated second law. Furthermore, we establish a connection with information-theoretic quantities, in particular the Petz-R\'enyi divergences, and leverage this connection to derive upper and lower bounds. Finally, we decompose the entropy production into incoherent and coherent contributions, identifying distinctive features of the coherent term in the vicinity of exceptional points. We illustrate our results using a paradigmatic model of non-Hermitian evolution based on a two-level system.
Starting from the unitary evolution of a closed quantum system, we rigorously demonstrate that the projection of the global wavefunction onto an arbitrary local subsystem is governed by an exact, time-dependent non-Hermitian Schr\"odinger equation. Crucially, the derivation does not rely on conventional approximations...
Ling-Feng Liu, Wei-Wei Yang, Jiang-Ping Hu et al.· 1 citation· ⚡1
In this study, we use the harmonic oscillator’s energy spectrum to connect its dynamical behavior to the formalism of statistical mechanics through entropy. We perform a thermal analysis of the entropy generated by this spectrum in both commutative and noncommutative two-dimensional configuration spaces, employing the...
J. Sadeghi, M. A. S. Afshar, H. Z. Kalbasti et al.· Physica Scripta· 0 citations
We propose a new product entropy, defined as the R\'enyi (or von Neumann) entropy of a normalized product operator constructed from two density matrices. We establish a duality showing that the SVD entanglement entropy of a subsystem for two pure states is exactly equivalent to the product entropy of the complementary...
Jiaju Zhang, Zhuo-Yu Xian, René Meyer et al.· 0 citations
This paper derives a multiscale Bakry-\'Emery criterion for an upper bound on the Araki relative entropy of perturbations of an equilibrium state in relativistic QFT. Using stochastic positivity, affiliated perturbations of the relativistic bosonic field can be put in correspondence with perturbations of the massive Eu...
In a quantum system initially in the $n$-th eigenstate, an adiabatic evolution of the Hamiltonian ensures that the system remains in the corresponding instantaneous eigenstate while acquiring a phase factor. This phase has two components: one resulting from standard time evolution and another associated with the depend...
Mustapha Maamache· Revista mexicana de física· 0 citations
Correlation functions are central to understanding the behavior of quantum systems, with their spectra giving direct access to quasiparticle and collective excitations. However, the long-time evolution required for sufficient spectral resolution is challenging to reach for both classical and quantum simulations. In thi...
F. Gambetta, S. Wang, R. A. Santos· 0 citations
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