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Restoring Landauer's Principle for Unitarily Transformed Thermal Reservoirs

Hao Xu

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.

Restoring Landauer's Principle for Unitarily Transformed Thermal Reservoirs

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.
Paper Structure (2 sections, 1 theorem, 37 equations)

This paper contains 2 sections, 1 theorem, 37 equations.

Table of Contents

  1. Proof of Theorem 1
  2. Derivation of Eq. \ref{['ep']}

Key Result

Theorem 1

Let $\rho_{SR} = \rho_S \otimes \rho_R$ be a product state on a bipartite system $SR$, where $\rho_R = \hat{O} \frac{\mathrm e^{-\beta \hat{H}_R}}{\operatorname{tr}[\mathrm e^{-\beta \hat{H}_R}]} \hat{O}^\dagger$ is obtained from the thermal state at inverse temperature $\beta$ by applying a unitary where $\hat{H}_{\mathrm{eff}}:= \hat{O} \hat{H}_{R} \hat{O}^{\dagger}$, $\Delta S:=S(\rho_S)-S(\rho

Theorems & Definitions (2)

  • Theorem 1
  • proof