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arXiv:2602.04552

Restoring Landauer's Principle for Unitarily Transformed Thermal Reservoirs

Hao Xu

quant-phgr-qchep-thSubmitted Feb 4, 2026• Announced Feb 5, 2026• 0 citations
v1 · Feb 4, 2026v2 · May 7, 2026
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Abstract

Landauer's principle, a cornerstone of quantum information and thermodynamics, appears to be violated when the thermal reservoir is replaced by a squeezed thermal state (STS). We introduce a formal extension of the principle to such unitarily transformed thermal states. By defining an effective Hamiltonian, we rigorously establish a generalized Landauer inequality, which naturally reduces to the standard case for an ordinary thermal reservoir as a special instance. The framework further yields a consistent definition of entropy production and a proof of its non-negativity. We illustrate its utility by studying an arbitrarily moving Unruh-DeWitt detector coupled to a quantum field initially prepared in the STS. Using perturbation theory, we compute the entropy production explicitly, confirming its positivity. As a result of the symmetry breaking induced by the unitary transformation, it depends on both the proper time interval and the absolute spacetime position. Our work resolves the apparent violation of Landauer's principle with STSs. It also provides a robust tool for analyzing quantum thermodynamics in non-equilibrium and relativistic settings, with potential implications for quantum thermal machines and information protocols.

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Landauer's principle, a cornerstone of quantum information and thermodynamics, appears to be violated when the thermal reservoir is replaced by a squeezed thermal state (STS). We introduce a formal extension of the principle to such unitarily transformed thermal states. By defining an effective Hamiltonian, we rigorously establish a generalized Landauer inequality, which naturally reduces to the standard case for an ordinary thermal reservoir as a special instance. The framework further yields a consistent definition of entropy production and a proof of its non-negativity. We illustrate its utility by studying an arbitrarily moving Unruh-DeWitt detector coupled to a quantum field initially prepared in the STS. Using perturbation theory, we compute the entropy production explicitly, confirming its positivity. As a result of the symmetry breaking induced by the unitary transformation, it depends on both the proper time interval and the absolute spacetime position. Our work resolves the apparent violation of Landauer's principle with STSs. It also provides a robust tool for analyzing quantum thermodynamics in non-equilibrium and relativistic settings, with potential implications for quantum thermal machines and information protocols.
We study quantum thermodynamics in nonequilibrium reservoirs (NERs) that are prepared from initially thermal ones via unitary driving processes. Based on the formulation of entropy production in NERs, we establish a Landauer-like bound and show that the bound can be violated under a definite condition depending on the states of NERs. It is found that the breakdown of this Landauer-like bound implies occurrences of several anomalous phenomena in NERs, namely, the efficiency enhancement of quantum thermal machines beyond the Carnot limit, the extraction of work from a single reservoir, and the spontaneous heat flow from a cold reservoir to a hot one. The results are illustrated through a physical model taking the preparation processes of NERs into account. Our work sheds light on the reason and condition of some unusual phenomena occurring in NERs and is helpful for one to prepare effective NERs that can be used as quantum resources to realize certain thermodynamic tasks.
The first law of thermodynamics, which governs energy conservation, is traditionally formulated as an equality. Surprisingly, we demonstrate that the first law alone implies a universal Landauer-like inequality linking changes in system entropy and energy. However, contrasting with the Landauer principle derived from the second law of thermodynamics, our obtained Landauer-like inequality solely relies on system information and is applicable in scenarios where implementing the Landauer principle becomes challenging. Furthermore, the Landauer-like inequality can complement the Landauer principle by establishing a dual {\it upper} bound on heat dissipation. We illustrate the practical utility of the Landauer-like inequality in dissipative quantum state preparation and quantum information erasure applications. Our findings offer new insights into identifying thermodynamic constraints relevant to the fields of quantum thermodynamics and the energetics of quantum information processing and more specifically, this approach could facilitate investigations into systems coupled to non-thermal baths or scenarios where access to bath information is limited.
The concept of thermal information conservation offers a new perspective on the interplay between thermodynamics and quantum information theory. In this work we introduce the thermal information quantity Q_T, defined for an isolated quantum system as the negative logarithm of the density of states weighted by the Boltzmann factor. We demonstrate that Q_T behaves as a conserved quantity during unitary evolution under a broad class of Hamiltonians that respect a hidden symmetry connecting energy and entropy. By establishing a rigorous link between Q_T and the von Neumann entropy, we show that the standard second law of thermodynamics can be viewed as a special case of a more general conservation principle. The implications of this principle for the design of quantum thermal engines, error‑free quantum memory, and the fundamental limits of heat transport are discussed. The framework also provides a natural bridge between classical thermodynamic irreversibility and quantum reversibility, suggesting that the apparent arrow of time in macroscopic systems may emerge from constraints on Q_T rather than from entropy production alone. Keywords: Thermal information, quantum thermodynamics, conservation law, entropy, quantum engines.
The erasure of quantum information is governed by two fundamental thermodynamic bounds: Landauer’s principle, which establishes the absolute minimum energetic cost of resetting a state, and Nernst’s unattainability principle, which dictates that perfect cooling to absolute zero entropy requires infinite resources. Under finite constraints, conventional cooling protocols utilizing thermal baths composed of n non-interacting particles are bottlenecked by a linear dissipation barrier (O(1/n)). In this thesis, we establish the ultimate thermodynamic limits of finite-resource multiqubit erasure and introduce the most thermodynamically efficient cooling protocol currently known. Building upon the max-cooling framework—a global unitary operation that systematically sorts the eigenvalues of the joint system-bath state to pack the highest probability mass into the target’s ground state—we engineer a bath Hamiltonian with specific, target-dependent degeneracies for arbitrary m-qubit systems. This collective protocol achieves an optimal asymptotic entropy production scaling of Σ = O(mˆ2/nˆ2), successfully saturating the scaling of the fundamental theoretical lower bound. This degeneracy-optimized approach strictly outperforms both standard non-interacting reservoirs and the best-known protocol for the independent cooling of single qubits using a reservoir of interacting particles (O(mˆ3/nˆ2)). Furthermore, we establish that surpassing conventional dissipation barriers requires an operational threshold of just n ≥ 2mˆ2 bath particles to achieve this optimal scaling.
We investigate the link between information and thermodynamics embodied by Landauer's principle in the open dynamics of a multipartite quantum system. Such irreversible dynamics is described in terms of a collisional model with a finite temperature reservoir. We demonstrate that Landauer's principle holds, for such a configuration, in a form that involves the flow of heat dissipated into the environment and the rate of change of the entropy of the system. Quite remarkably, such a principle for heat and entropy power can be explicitly linked to the rate of creation of correlations among the elements of the multipartite system and, in turn, the non-Markovian nature of their reduced evolution. Such features are illustrated in two exemplary cases.
We expand the standard thermodynamic framework of a system coupled to a thermal reservoir by considering a stream of independently prepared units repeatedly put into contact with the system. These units can be in any nonequilibrium state and interact with the system with an arbitrary strength and duration. We show that this stream constitutes an effective resource of nonequilibrium free energy and identify the conditions under which it behaves as a heat, work or information reservoir. We also show that this setup provides a natural framework to analyze information erasure ("Landauer's principle") and feedback controlled systems ("Maxwell's demon"). In the limit of a short system-unit interaction time, we further demonstrate that this setup can be used to provide a thermodynamically sound interpretation to many effective master equations. We discuss how non-autonomously driven systems, micromasers, lasing without inversion, and the electronic Maxwell demon, can be thermodynamically analyzed within our framework. While the present framework accounts for quantum features (e.g. squeezing, entanglement, coherence), we also show that quantum resources do not offer any advantage compared to classical ones in terms of the maximum extractable work.