A Generalized Landauer's Principle for Unitarily Transformed Thermal Reservoirs

TL;DR

This paper extends Landauer's principle to unitarily transformed thermal reservoirs, such as squeezed thermal states, establishing a generalized inequality and confirming the positivity of entropy production in these non-standard quantum thermodynamic scenarios.

Contribution

It introduces a formal framework with an effective Hamiltonian to generalize Landauer's principle for transformed thermal states, resolving apparent violations and enabling analysis in relativistic quantum thermodynamics.

Findings

Generalized Landauer inequality for unitarily transformed thermal states

Explicit calculation of entropy production confirming its positivity

Framework applicable to non-equilibrium and relativistic quantum thermodynamics

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), owing to the additional thermodynamic resources inherently present in the squeezed state. 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.