[Paper Review] Quantum Frame Relativity of Subsystems, Correlations and Thermodynamics

Philipp A. Hoehn, Isha Kotecha+1 more|arXiv (Cornell University)|Aug 17, 2023

Mechanical and Optical Resonators4 citations

TL;DR

This paper establishes that quantum reference frames (QRFs) induce a relativity of subsystems, correlations, and thermodynamics, analogous to the relativity of simultaneity in special relativity. It demonstrates that subsystem entropies, temperatures, heat, work, and entropy production are QRF-dependent, with QRF transformations capable of mapping positive to negative temperature states—offering a relational, frame-dependent foundation for quantum thermodynamics and information theory in gauge and gravitational contexts.

ABSTRACT

It was recently noted that different internal quantum reference frames (QRFs) partition a system in different ways into subsystems, much like different inertial observers in special relativity decompose spacetime in different ways into space and time. Here we expand on this QRF relativity of subsystems and elucidate that it is the source of all novel QRF dependent effects, just like the relativity of simultaneity is the origin of all characteristic special relativistic phenomena. We show that subsystem relativity, in fact, also arises in special relativity with internal frames and, by implying the relativity of simultaneity, constitutes a generalisation of it. Physical consequences of the QRF relativity of subsystems, which we explore here systematically, and the relativity of simultaneity may thus be seen in similar light. We focus on investigating when and how subsystem correlations and entropies, interactions and types of dynamics (open vs. closed), as well as quantum thermodynamical processes change under QRF transformations. We show that thermal equilibrium is generically QRF relative and find that, remarkably, QRF transformations not only can change a subsystem temperature, but even map positive into negative temperature states. We further examine how non-equilibrium notions of heat and work exchange, as well as entropy production and flow depend on the QRF. Along the way, we develop the first study of how reduced subsystem states transform under QRF changes. Focusing on physical insights, we restrict to ideal QRFs associated with finite abelian groups. Besides being conducive to rigour, the ensuing finite-dimensional setting is where quantum information-theoretic quantities and quantum thermodynamics are best developed. We anticipate, however, that our results extend qualitatively to more general groups and frames, and even to subsystems in gauge theory and gravity. [abridged]

Motivation & Objective

• To establish the relativity of subsystems under quantum reference frame (QRF) transformations as a foundational principle, analogous to the relativity of simultaneity in special relativity.
• To investigate how QRF transformations affect subsystem correlations, entanglement entropy, and thermodynamic quantities such as heat, work, and entropy production.
• To demonstrate that thermal equilibrium and Gibbs states are not absolute but depend on the choice of QRF, including the possibility of QRF-dependent negative temperature states.
• To develop a formalism for how reduced subsystem states transform under QRF changes, showing non-unitary transformation in the generic case.
• To extend the framework to gauge theories and gravity by proposing a relational definition of subsystems based on QRF-relative observables, moving beyond region-based locality.

Proposed method

• Adopt a perspective-neutral formalism using finite-dimensional, abelian group-based ideal QRFs to ensure mathematical rigor and compatibility with quantum information theory.
• Define subsystems via QRF-dependent subalgebras of gauge-invariant observables, distinguishing between relational observables (invariant under QRF changes) and subsystem-specific operators.
• Construct QRF transformations via symmetry-induced unitary maps that reassign the decomposition of the total Hilbert space into subsystems S and 'the other frame'.
• Analyze the transformation of reduced density matrices under QRF changes, showing they transform non-unitarily in general, which underlies the frame dependence of entropies and correlations.
• Apply the formalism to thermodynamic processes by defining QRF-relative heat, work, and entropy flow using initial product states and energy balance relations.
• Use algebraic techniques to identify TPS-invariant (tensor product structure) subalgebras and operators, isolating quantities that remain invariant under QRF changes.

Experimental results

Research questions

• RQ1 How do subsystem decompositions, correlations, and entanglement entropy transform under changes of quantum reference frame?
• RQ2 To what extent are thermodynamic quantities such as heat, work, and entropy production dependent on the choice of quantum reference frame?
• RQ3 Can QRF transformations map a system from a positive to a negative temperature state, and what does this imply for thermal equilibrium?
• RQ4 How do reduced subsystem states and their associated entropies transform under QRF changes, and why is this transformation non-unitary in general?
• RQ5 Can a relational, frame-dependent definition of subsystems and entanglement entropy be consistently formulated in gauge theories and gravity, replacing region-based locality?

Key findings

• Subsystem decompositions, correlations, and entanglement entropy are inherently frame-dependent under QRF transformations, with distinct values arising in different QRFs.
• Thermal equilibrium and Gibbs states are not absolute but depend on the choice of QRF, with QRF transformations capable of converting positive-temperature states into negative-temperature states.
• Reduced subsystem states transform non-unitarily under QRF changes, which explains the frame dependence of entropies and correlations.
• Heat, work, and entropy production in thermodynamic processes are QRF-relative, with initial product states required for consistency, and fluctuation theorems like the Jarzynski equality becoming frame-dependent.
• The formalism reveals that the relativity of subsystems generalizes the relativity of simultaneity in special relativity, with both phenomena arising from the same underlying structure of frame-dependent decomposition.
• A relational definition of subsystems based on QRF-relative observables offers a viable alternative to region-based locality in gauge and gravitational theories, with edge modes playing a key role as dynamical QRFs.