Measurements Alone Can Power Engines, Reveals New Quantum Theory

Scientists have long considered measurement a passive act, but recent theoretical work demonstrates measurements can inject energy into systems, powering engines fuelled entirely by measurement processes. Robert Czupryniak (University of Rochester), Bibek Bhandari (Chapman University), Paolo Andrea Erdman (Freie Universität Berlin) and Andrew N Jordan et al. present a universal theory characterising these ‘vacuum measurement engines’ through the introduction of the vacuum bending function (QVBF). This novel quantity describes how interactions lower ground-state energy, and crucially, the researchers demonstrate that thermodynamic observables, including work and efficiency, are governed solely by the QVBF’s shape, independent of underlying microscopic details. By establishing a link between work fluctuations, QVBF curvature, and a generalised fluctuation relation involving Fisher information, this work provides a fundamental framework for understanding and optimising energy extraction from the quantum vacuum.

Ground-state energy landscape dictates performance of quantum vacuum engines, fundamentally limiting their efficiency

Scientists have uncovered a fundamental principle governing quantum vacuum measurement engines, demonstrating that their thermodynamic performance is dictated entirely by the shape of the system’s ground-state energy landscape. This work introduces the quantum vacuum bending function (QVBF), a novel quantity characterizing how interactions lower the ground-state energy, and reveals its surprising centrality to understanding these engines.
Researchers established that all thermodynamic observables, including work and efficiency, are governed solely by the QVBF’s form, irrespective of the underlying microscopic details of the system. The study details a general theory of vacuum measurement engines, moving beyond model-specific analyses to identify unifying features relevant to thermodynamic performance across diverse physical platforms.

By introducing the QVBF, the team provides a broadly applicable theoretical perspective that clarifies the fundamental thermodynamic role of many-body structure. Exactly solvable models and numerical simulations, encompassing both single and many-body systems, confirm the theory and illustrate how the QVBF alone determines the performance of these quantum engines.

Furthermore, the research demonstrates that fluctuations in work are defined by the curvature of the QVBF, modulated by a model-dependent quantity. These fluctuations are constrained by a generalized fluctuation relation linking Fisher information and the ground-state energy landscape. This connection between thermodynamic noise and the geometry of the ground state establishes a new understanding of quantum thermodynamic limits.

The findings establish a universal and experimentally relevant characterization of vacuum measurement engines, offering guidance for designing future quantum technologies. This framework has been successfully applied to representative examples based on qubits and harmonic oscillators, demonstrating its versatility across distinct physical platforms.

The work reveals that measurements applied to a many-body system in its ground state can extract work even at zero temperature, exploiting the energetic potential of the quantum vacuum. By expressing quantum Fisher information in terms of experimentally accessible quantities, the research provides a practical route to establishing fundamental bounds on quantum metrological sensitivity and advancing the field of quantum thermodynamics.

Derivation of ground state overlap and perturbation response are key to accurate modeling

Measurements can inject energy into systems, enabling engines whose operation is powered entirely by measurements. This work develops a general theory of vacuum measurement engines by introducing the vacuum bending function (QVBF), a quantity that characterizes the lowering of the ground-state energy due to interactions.

The research demonstrates that all thermodynamic observables, including work and efficiency, are governed solely by the shape of the ground-state energy landscape encoded in the QVBF, irrespective of microscopic details. To determine the fluctuations of the engine, calculations began by differentiating the norm ⟨0|0⟩= 1 with respect to λ, yielding 2 Re {⟨0|0′⟩} = 0.

This implied that the overlap of the ground state and its derivative must be purely imaginary, expressed as ⟨0|0′⟩= if(λ), where f(λ) is a real function. Subsequently, differentiating the eigenproblem H|0⟩= E0|0⟩ over λ resulted in H′|0⟩+ H|0′⟩= E′ 0|0⟩+ E0|0′⟩. Applying the eigenstate ⟨n| of the total Hamiltonian H(λ) from the left produced ⟨n|H′|0⟩+ En⟨n|0′⟩= E0⟨n|0′⟩.

The study then derived an expression for |0′(λ)⟩, omitting the λ dependence for conciseness. The ground state derivative was expressed as |0′⟩= |0⟩⟨0|0′⟩+ X n>0 |n⟩⟨n|0′⟩ = if(λ)|0⟩− X n>0 |n⟩⟨n|Hint|0⟩ En −E0. Evaluating ⟨0′|0′⟩ resulted in ⟨0′|0′⟩= f(λ)2 + X n>0 |⟨n|Hint|0⟩|2 (En −E0)2.

The second derivative of the ground state energy was obtained via the Hellmann-Feynman theorem, E′ 0 = ⟨0|Hint|0⟩, and further differentiated to give E′′ 0 = (⟨0|Hint|0⟩)′, which equals −2X n>0 |⟨n|Hint|0⟩|2 En −E0. Researchers calculated the variance of the interaction Hamiltonian, defining H2 int = X n ⟨0|Hint|n⟩⟨n|Hint|0⟩, and subsequently derived H2 int −⟨Hint⟩2 = X n>0 |⟨n|Hint|0⟩|2.

This led to the expression for the variance of the work output, σ2 = H2 loc λ −⟨Hloc⟩2 λ = λ2 H2 int λ −⟨Hint⟩2 λ, which was then connected to σ2 = λ2X n>0 |⟨n|Hint|0⟩|2. Defining cn ≡|⟨n|Hint|0⟩| and en ≡En −E0, the study established σ2 = 1 2λ2∆′′ e, demonstrating that fluctuations are defined by the curvature of the QVBF modulated by a model-dependent quantity, ‘e’. Exactly solvable models and numerical simulations confirmed the theory and illustrated how the QVBF alone determines the performance of vacuum measurement engines.

Quantum vacuum bending function governs performance of measurement-powered engines by dictating energy extraction efficiency

Measurements can inject energy into systems, enabling engines whose operation is powered entirely by measurements. This work introduces the quantum vacuum bending function (QVBF), a quantity characterizing the lowering of ground-state energy due to interactions, and develops a general theory of vacuum measurement engines.

Thermodynamic observables, including work and efficiency, are governed solely by the shape of the ground-state energy landscape encoded in the QVBF, irrespective of microscopic details. Work fluctuations are determined by the curvature of the QVBF modulated by a model-dependent quantity, and are constrained by a generalized fluctuation relation involving Fisher information and the ground-state energy landscape.

Exactly solvable models and numerical simulations of single and many-body systems confirm the theory, illustrating that the QVBF alone determines the performance of vacuum measurement engines. The curvature of the QVBF sets the scale for thermodynamic noise, establishing a direct connection between this noise and the geometry of the ground-state energy landscape.

An effective thermodynamic uncertainty relation is derived, bounding work fluctuations in terms of the quantum Fisher information. Expressing the quantum Fisher information using experimentally accessible quantities such as work and its fluctuations provides a practical route to establishing fundamental bounds on quantum metrological sensitivity.

The expected work per cycle is calculated as P n |⟨0(λ)|n(0)⟩|2(En(0) −E0(0)) which simplifies to ⟨Hloc⟩λ −E0(0). Quantum heat, defined as the average energy injected into the system by the measurement apparatus per cycle, is quantified as −λ⟨Hint⟩λ. The engine’s efficiency is then calculated as W(λ)/Q(λ), while the fluctuations of the engine’s work per cycle are given by ⟨H2 loc⟩λ −⟨Hloc⟩2 λ.

The QVBF, defined as ∆(λ) = E0(0) −E0(λ), represents the coupling-induced lowering of the ground-state energy. All thermodynamic quantities, W(λ), Q(λ), and η(λ), depend only on the QVBF and its derivative, with fluctuations dependent on its curvature up to a model-dependent function. Work fluctuations are found to be σ2(λ) = 1 2λ2∆′′(λ) e(λ), where e(λ) is a function determined by matrix elements of Hint. Fundamental bounds on work fluctuations are established as λ2∆′′(λ) emin 2 ≤σ2(λ) ≤λ2∆′′(λ) emax 2, dependent on the minimum and maximum excitation energies accessible through Hint.

Ground-state curvature dictates performance of vacuum measurement engines, fundamentally limiting sensitivity

Scientists have established a comprehensive theory describing how energy can be extracted from systems solely through measurement. This work introduces the quantum vacuum bending function, a key quantity defining the ground-state energy landscape and governing all thermodynamic aspects of vacuum measurement engines.

The research demonstrates that work output, efficiency, and fluctuations are determined by the shape and curvature of this landscape, independent of the specific microscopic details of the system. Further investigation using both analytical models and numerical simulations of qubit and harmonic oscillator systems confirms that the quantum vacuum bending function accurately predicts engine performance.

Specifically, the rate of work change is directly linked to the curvature of the ground-state energy landscape. Comparisons between qubit-based and oscillator-based engines reveal distinctions in their behaviour, with qubit systems exhibiting work saturation due to the bounded nature of their interaction Hamiltonian, while oscillator systems do not.

The authors acknowledge a limitation in that the theoretical framework relies on a nondegenerate ground state, a condition verified in their simulations. Future research could explore the behaviour of these engines in systems with more complex ground states or investigate the potential for optimising engine performance by tailoring the shape of the quantum vacuum bending function. These findings establish a geometrical understanding of quantum measurement engines and offer a pathway toward designing efficient energy-harvesting technologies based on measurement principles.