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arXiv:2609.06185

Heat distribution of quantum fields interacting with Unruh-DeWitt detectors

Marcos L. W. Basso, Alberto Saa

gr-qchep-thquant-phSubmitted Sep 5, 2026• Announced Sep 8, 2026
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Abstract

We introduce an operational framework for heat-exchange statistics between a quantum field and an Unruh-DeWitt detector in Minkowski spacetime. Using an interferometric protocol, we define the characteristic function of heat without projective measurements, consistently with relativistic causality. We derive perturbative expressions for this function and the heat distribution. In the vacuum, the statistics coincides with the low-intensity expansion of a unidirectional Poisson law, while for Kubo-Martin-Schwinger (KMS) states it has a bidirectional Poisson structure up to second order in perturbation theory. We study how fluctuation relations emerge from detector properties and field correlations, identifying regimes where they reduce to known heat-exchange fluctuation relations. We derive the entropic Landauer inequality as a specialization of the algebraic entropy-balance theorem of Jakšić and Pillet and verify it numerically within the perturbative detector-field interaction. We compare its tightness with a complementary Landauer bound derived from the full counting statistics of heat, analyzing their dependence on the detector's initial state and interaction time. We also formulate the first and second laws for the explicitly switched detector-field dynamics, identifying the external switching work that reconciles the field-energy gain with the detector-energy change. In the gapless and delta-switching regimes, where the dynamics admits a non-perturbative treatment, the characteristic function coincides with that of a bidirectional Poisson process, yielding an exact fluctuation theorem determined by the KMS condition. These results provide a consistent framework for heat statistics in relativistic quantum field theory and clarify the emergence of fluctuation relations.

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We introduce an operational framework for heat-exchange statistics between a quantum field and an Unruh-DeWitt detector in Minkowski spacetime. Using an interferometric protocol, we define the characteristic function of heat without projective measurements, consistently with relativistic causality. We derive perturbative expressions for this function and the heat distribution. In the vacuum, the statistics coincides with the low-intensity expansion of a unidirectional Poisson law, while for Kubo-Martin-Schwinger (KMS) states it has a bidirectional Poisson structure up to second order in perturbation theory. We study how fluctuation relations emerge from detector properties and field correlations, identifying regimes where they reduce to known heat-exchange fluctuation relations. We derive the entropic Landauer inequality as a specialization of the algebraic entropy-balance theorem of Jakšić and Pillet and verify it numerically within the perturbative detector-field interaction. We compare its tightness with a complementary Landauer bound derived from the full counting statistics of heat, analyzing their dependence on the detector's initial state and interaction time. We also formulate the first and second laws for the explicitly switched detector-field dynamics, identifying the external switching work that reconciles the field-energy gain with the detector-energy change. In the gapless and delta-switching regimes, where the dynamics admits a non-perturbative treatment, the characteristic function coincides with that of a bidirectional Poisson process, yielding an exact fluctuation theorem determined by the KMS condition. These results provide a consistent framework for heat statistics in relativistic quantum field theory and clarify the emergence of fluctuation relations.
We investigate when temporal ordering becomes operationally meaningful in relativistic quantum field theory using localized detector models. A time parameter alone does not ensure that different sequences of operations are physically distinguishable. We show that distinguishability arises when the state satisfies the Kubo--Martin--Schwinger (KMS) condition and the detector couples through non-commuting observables. We consider uniformly accelerated two-level detectors interacting with a quantum field in the Minkowski vacuum. The restriction of the vacuum to the detector trajectory induces a thermal response characterized by the Unruh temperature and the Tolman profile. For sequential couplings through distinct observables, the reduced detector state depends on the ordering of interactions already at second order, with a dependence controlled by the KMS parameter. This asymmetry is quantified using quantum relative entropy. In a minimal model, the relevant states form a family of non-commuting Gibbs states with identical spectra and different generators, yielding a closed-form expression depending only on the dimensionless combination of temperature and detector energy scale.
Abstract This investigation focuses on studying the dynamics of entropy disorder and quantum correlations between two detectors interacting with a scalar field in a four-dimensional Minkowski space-time using the Unruh-deWitt model. The aim is to gain insights into the evolution of quantum resources in uniformly accelerated detectors that interact with a massless scalar field. To achieve this, useful metrics such as local quantum Fisher information (LQFI), quantum consonance, and linear entropy are employed to analyze the quantum correlations and entropy disorder. The results indicate that the quantum correlations are heavily reliant on the choice of the initial state of the detectors. Interestingly, the quantum correlations exhibit a surprising resurgence as the Unruh temperature increases for specific initial state parameters. However, for other values, the Unruh temperature takes over and leads to a monotonic decrease in the quantum correlations. In addition, the degree of disorder is observed to increase as the Unruh temperature increases. Furthermore, the investigation delves into how the energy spacing of the detector affects quantum correlations across various initial state parameters. Further elucidating the behavior of quantum resources in curved space-time, we demonstrate that some initial state parameters can cause sudden changes in correlation measures as a function of energy spacing. These results highlight the relevance of choosing adequate initial state parameters, as they have a significant impact on the variation of quantum resources in two Unruh-deWitt detectors.
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We investigate the statistics of heat exchange between a finite system coupled to reservoir(s). We have obtained analytical results for heat fluctuation theorems in the transient regime considering the Hamiltonian dynamics of the composite system consisting of the system of interest and the heat bath(s). The system of interest is driven by an external protocol. We first derive it in the context of a single heat bath. The result is in exact agreement with known result. We then generalize the treatment to two heat baths. We further extend the study to quantum systems and show that relations similar to the classical case hold in the quantum regime. For our study we invoke von Neumann two-point projective measurement in quantum mechanics in the transient regime. The study of quantum systems follows the same lines of argument as that of the classical system, and as a result the treatment used in the latter complements that used in the former. Our result is a generalization of Jarzynski-Wòjcik heat fluctuation theorem.
We review Unruh–DeWitt detectors and other models of detector–field interaction in a relativistic quantum field theory setting as a tool for extracting detector–detector, field–field and detector–field correlation functions of interest in quantum information science, from entanglement dynamics to quantum teleportation. In particular, we highlight the contrast between the results obtained from linear perturbation theory which can be justified provided switching effects are properly accounted for, and the nonperturbative effects from available analytic expressions which incorporate the backreaction effects of the quantum field on the detector behavior.
In this thesis interacting relativistic and non relativistic Quantum Field Theories (QFT) are studied, investigating their equilibrium configurations and their long time evolution in the framework of perturbative Algebraic Quantum Field Theory, studying also convergence in a specific model. In the first part, concerning the relativistic case, we study, in formal perturbation theory, interacting KMS states generalising results by Fredenhagen and Lindner to fermionic field theories. As an application their stability is investigated together with the characterisation of the Debye screening effect in plasmas via the explicit solution of the Semiclassical Maxwell equations. Connected to these results, we also initiate a systematic study of secular growths appearing in the truncated perturbative series and affecting the validity of perturbation theory in its long time predicting capability. We restrict to theories on Minkowski spacetime and provide, for interactions depending on time via a switching process, a sufficient condition preventing secular growths in the truncated perturbative series. In the second part, we focus on a model of non relativistic quantum field theory. We construct equilibrium states at positive temperature in the presence of a condensation phase for a gas of non relativistic Bose particles on an infinite space interacting through a localised two body interaction. The convergence is proven, both for the interacting KMS state and for the entropy of the interacting KMS state relative to the free KMS state. The strategy of our proof combines ideas of Algebraic QFT, Constructive QFT and methods of statistical mechanics in the operator algebraic setting. Limits where the localisation of the two-body interaction is removed are eventually discussed, in combination with limits of the other physical parameters of the theory such as temperature, strength of the interaction and chemical potential. Finally, in the appendix, we present results on the Araki-Uhlmann relative entropy in fermionic quantum field theories, as well as an entropy-area relation, obtained via semiclassical methods, for the cosmological horizon in the static patch of de Sitter spacetime sourced by a coherent excitation of a free quantum scalar field. This completes the collection of original results obtained during the PhD.