Entropic Fluctuation Theorems for the Spin-Fermion Model

We study entropic fluctuations in the Spin-Fermion model describing an $N$-level quantum system coupled to several independent thermal free Fermi gas reservoirs. We establish the quantum Evans-Searles and Gallavotti-Cohen fluctuation theorems and identify their link with entropic ancilla state tomography and quantum phase space contraction of non-equilibrium steady state. The method of proof involves the spectral resonance theory of quantum transfer operators developed by the authors in previous works.

💡 Research Summary

The paper investigates entropic fluctuations in the spin‑fermion model, a paradigmatic open quantum system consisting of an N‑level quantum system (the “spin”) coupled to several independent thermal reservoirs modeled as free Fermi gases. The authors rigorously establish the quantum Evans‑Searles and Gallavotti‑Cohen fluctuation theorems for this model, thereby extending classical fluctuation results to a fully quantum, many‑body setting.

The model is defined on a C(^*)‑algebraic framework. The small system (S) has a finite‑dimensional Hilbert space (K_S) and Hamiltonian (H_S); its observable algebra is (\mathcal O_S = B(K_S)) with the tracial reference state (\omega_S). Each reservoir (R_j) is described by a CAR algebra (\mathcal O_j = \mathrm{CAR}(h_j)) built from a single‑particle Hilbert space (h_j) and a one‑particle Hamiltonian (h_j). The reservoirs are in gauge‑invariant quasi‑free KMS states (\omega_j) at inverse temperatures (\beta_j). The total algebra is (\mathcal O = \mathcal O_S \otimes \bigotimes_{j=1}^M \mathcal O_j) with reference state (\omega = \omega_S \otimes \bigotimes_j \omega_j).

Interactions are of the form
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