Fluctuation-Induced Angular-Momentum Transfer

• Fluctuation-Induced Angular-Momentum Transfer is the process by which angular momentum is redistributed via fluctuating carriers such as photons, magnons, and phonons, rather than through direct mechanical contact.
• Key methodologies involve theoretical modeling and nanoscale experiments, including electromagnetic near-field studies, Casimir torque measurements, and spin-lattice dynamics to reveal synchronization and fluctuation pumping.
• This phenomenon spans applications from nanoparticle dynamics to astrophysical turbulence, with quantified insights such as five orders-of-magnitude differences in coupling and temperature-dependent torque behaviors.

Fluctuation-induced angular-momentum transfer denotes the exchange, redistribution, or fluctuation growth of angular momentum through vacuum, thermal, quantum, or turbulent fluctuations rather than through direct mechanical contact. Across fluctuational electrodynamics, spin transport, spin-lattice dynamics, phonon physics, turbulence, and high-energy nuclear theory, the transferred quantity can be the mechanical angular momentum of rigid-body rotation, spin angular momentum, orbital angular momentum, phonon pseudo angular momentum, or the variance of total angular momentum itself (Sanders et al., 2018, Maghrebi et al., 2018, Nishikawa et al., 2021, Minakova et al., 14 Mar 2025, Yi et al., 26 Jun 2025).

1. Conceptual scope and conservation structure

A common structural feature is that angular momentum is not treated as an isolated mechanical observable but as a quantity partitioned among matter, fields, and internal collective modes. In rotating nanoparticle chains, angular momentum can flow between a particle and the environment, producing vacuum or thermal rotational friction, and also between different particles, producing mutual dissipative coupling and synchronization. In early-time Glasma dynamics and in the phonon vacuum of symmetric crystals, by contrast, the mean angular momentum can remain zero while the variance or finite-frequency susceptibility grows, so the relevant effect is fluctuation pumping rather than a nonzero mean torque (Sanders et al., 2018, Pooja et al., 2022, Yi et al., 26 Jun 2025).

The literature therefore supports two technically distinct but related usages. One concerns the transport of a nonzero mean angular-momentum current, torque, or rotation rate. The other concerns the generation of angular-momentum fluctuations, anisotropies, or response functions that can subsequently couple to another subsystem. This suggests that “transfer” is often mediated by a fluctuating carrier—photons, magnons, phonons, turbulent stresses, or gauge fields—even when the directly observable quantity is only a variance, a susceptibility, or a stochastic trajectory rather than a steady macroscopic rotation (Pooja et al., 2022, Yi et al., 26 Jun 2025, Charnotskii, 2018).

Conservation laws remain central throughout. The transferred angular momentum is stored, at different stages, in electromagnetic fields, lattice vibrations, magnons, rigid-body motion, Reynolds or Maxwell stresses, or orbital motion of probes. Several works are explicitly framed as bookkeeping problems: Casimir torque separates environment-mediated and particle-particle channels; Einstein–de Haas dynamics separates spin loss from mechanical gain; radiative theories track angular-momentum flux through the Maxwell stress tensor; and Glasma or turbulent theories identify the specific fluctuating stress component that carries the conserved quantity (Sanders et al., 2018, Nishikawa et al., 2021, Gao et al., 2020, Fries et al., 2017).

2. Electromagnetic near-field transport and Casimir torque

In nanoscale fluctuational electrodynamics, a direct realization is provided by a linear chain of $N$ spherical nanoparticles rotating about the chain axis. In that system the Casimir torque on particle $i$ is written as

$$M_i=\langle \mathbf p_i(t)\times \mathbf E_i(t)\rangle\cdot \hat{\mathbf z}, \qquad M_i=M_i^+-M_i^-,$$

so the transfer is explicitly the difference between opposite circular-polarization channels. For equal particle and environment temperatures, and in the experimentally relevant low-rotation regime, the rotational dynamics reduces to

$\dot{\Omega}_i=\sum_{j=1}^N H_{ij}\Omega_j,$

with diagonal terms representing rotational friction against the environment and off-diagonal terms representing many-body mutual torque coupling. For SiC nanospheres with $D=10$ nm and $d=1.5D$, the environment contribution is about five orders of magnitude smaller than the particle-particle coupling, the uniform collective mode decays very slowly with $\lambda_1\sim -10^{-6}\,\mathrm{s}^{-1}$, the other modes decay on the order of $1\,\mathrm{s}^{-1}$, and the resulting dynamics includes synchronization, mode-selected redistribution, driven steady-state angular-momentum conduction, and a rattleback-like sign reversal in nonuniform chains (Sanders et al., 2018).

A different electromagnetic nonequilibrium channel appears when a dc current biases graphene. There the drift current produces nonequilibrium fluctuations even at equal temperatures because the fluctuating radiation acquires a Doppler-shifted occupation

$$n_g(\omega,q_x)=\frac{1}{e^{\hbar(\omega-q_x v_d)/k_B T_e}-1},$$

so energy, linear momentum, and angular momentum can be transferred without a temperature bias. For an isotropic nanoparticle above the sheet, the spectral in-plane torque is

$$m_y(\omega)= -\hbar \,\mathrm{Im}[\alpha(\omega)] \int\frac{d^2\mathbf q}{(2\pi)^2} q_x\,\mathrm{Im}\!\big(r_p e^{2i\beta_0 d}\big)\, \delta n(\omega,q_x),$$

and its sign is fixed by the spin-momentum locking of current-biased graphene SPPs: a current along $i$0 yields an in-plane torque perpendicular to the current, along $i$1 in the paper’s convention. The torque is plasmon-mediated, finite at $i$2, nonmonotonic in $i$3, and remains within the same order when a temperature difference is added, even though the energy transfer can increase by about three orders of magnitude (Zhu et al., 2023).

3. Nonreciprocity, radiative torque, and equilibrium circulation

Nonreciprocity makes angular-momentum-resolved radiative transfer especially transparent. For a magnetically gapped topological-insulator thin film hotter than its environment, the emitted thermal photons are preferentially circularly polarized because the dissipative ac Hall conductivity weights the two helicity channels differently. The emitted angular-momentum flux is

$i$4

so the torque is a purely fluctuation-driven nonequilibrium response controlled by $i$5, whereas the energy radiation is controlled by $i$6. In the clean limit the torque scales as $i$7, behaves as $i$8 at high temperature, and is activated as $i$9 at low temperature (Maghrebi et al., 2018).

A separate equilibrium radiative effect occurs for two finite magneto-optical particles with misaligned gyrotropy axes. A single particle in thermal equilibrium emits no net angular momentum because particle and environment contributions cancel, but two particles at $$M_i=\langle \mathbf p_i(t)\times \mathbf E_i(t)\rangle\cdot \hat{\mathbf z}, \qquad M_i=M_i^+-M_i^-,$$0 can exchange angular momentum through the near field and experience equal magnitude torques with opposite signs that tend to align their gyrotropy axes parallel to each other. The formalism is expressed through the Maxwell-stress-based angular-momentum flux tensor $$M_i=\langle \mathbf p_i(t)\times \mathbf E_i(t)\rangle\cdot \hat{\mathbf z}, \qquad M_i=M_i^+-M_i^-,$$1, and for the subwavelength particles considered the transfer is stated to be dominated by spin angular momentum rather than orbital angular momentum (Gao et al., 2020).

In an explicitly angular-momentum-resolved Rytov formulation for nonreciprocal concentric cylinders, both heat and torque are written in terms of a spectral flux density $$M_i=\langle \mathbf p_i(t)\times \mathbf E_i(t)\rangle\cdot \hat{\mathbf z}, \qquad M_i=M_i^+-M_i^-,$$2, where each exchanged photon carries energy $$M_i=\langle \mathbf p_i(t)\times \mathbf E_i(t)\rangle\cdot \hat{\mathbf z}, \qquad M_i=M_i^+-M_i^-,$$3 and angular momentum $$M_i=\langle \mathbf p_i(t)\times \mathbf E_i(t)\rangle\cdot \hat{\mathbf z}, \qquad M_i=M_i^+-M_i^-,$$4. The net torque on the inner cylinder is

$$M_i=\langle \mathbf p_i(t)\times \mathbf E_i(t)\rangle\cdot \hat{\mathbf z}, \qquad M_i=M_i^+-M_i^-,$$5

In reciprocal media, $$M_i=\langle \mathbf p_i(t)\times \mathbf E_i(t)\rangle\cdot \hat{\mathbf z}, \qquad M_i=M_i^+-M_i^-,$$6 and the $$M_i=\langle \mathbf p_i(t)\times \mathbf E_i(t)\rangle\cdot \hat{\mathbf z}, \qquad M_i=M_i^+-M_i^-,$$7 and $$M_i=\langle \mathbf p_i(t)\times \mathbf E_i(t)\rangle\cdot \hat{\mathbf z}, \qquad M_i=M_i^+-M_i^-,$$8 channels cancel. Nonreciprocity breaks this symmetry, yields a propulsive torque already linear in the gyrotropic parameter, and simultaneously produces fluctuation-induced rotational friction. The same framework also predicts nonequilibrium Casimir repulsion strong enough to stabilize a contactless cylindrical heat engine, with efficiency remaining bounded by the Carnot limit (Shah et al., 23 Jun 2026).

The same nonreciprocal equilibrium circulation underlies a fluctuation-induced quantum analog of the Feynman disc paradox. A neutral magneto-optical or Weyl-semimetal nanoparticle can sustain a persistent equilibrium Poynting vector

$$M_i=\langle \mathbf p_i(t)\times \mathbf E_i(t)\rangle\cdot \hat{\mathbf z}, \qquad M_i=M_i^+-M_i^-,$$9

even though it carries no classical charge. When the source of nonreciprocity is removed, this field angular momentum is transferred to mechanical rotation. For a gyrotropic dipole the equilibrium flux is purely azimuthal, proportional to the off-diagonal polarizability $\dot{\Omega}_i=\sum_{j=1}^N H_{ij}\Omega_j,$0; for InSb at $\dot{\Omega}_i=\sum_{j=1}^N H_{ij}\Omega_j,$1, $\dot{\Omega}_i=\sum_{j=1}^N H_{ij}\Omega_j,$2, and $\dot{\Omega}_i=\sum_{j=1}^N H_{ij}\Omega_j,$3, the paper finds $\dot{\Omega}_i=\sum_{j=1}^N H_{ij}\Omega_j,$4 and an induced rotation $\dot{\Omega}_i=\sum_{j=1}^N H_{ij}\Omega_j,$5. The paper further states that the contribution of vacuum fluctuations dominates over thermal fluctuations at finite temperature (Biehs et al., 10 Sep 2025).

4. Spin exchange, stochastic transfer, and Einstein–de Haas conversion

A second major class replaces fluctuating photons by fluctuating spin-transfer events. In a spin-polarized dilute gas interacting with an optically trapped nanoparticle, interfacial spin tunneling generates a spin current

$\dot{\Omega}_i=\sum_{j=1}^N H_{ij}\Omega_j,$6

and angular-momentum conservation converts that spin loss of the gas into rigid-body rotation of the nanoparticle. Because the gas is dilute, the transfer is treated as a stochastic counting process. In the strongly polarized short-time limit the fluctuation dynamics reduces to the Ornstein–Uhlenbeck equation

$\dot{\Omega}_i=\sum_{j=1}^N H_{ij}\Omega_j,$7

and the mechanical response obeys

$\dot{\Omega}_i=\sum_{j=1}^N H_{ij}\Omega_j,$8

The deterministic Einstein–de Haas torque and the fluctuation-driven component are therefore generated by the same interfacial spin-exchange process, with the variance proposed as an inference route to the transfer rate (Nishikawa et al., 2021).

In metallic spin valves, a distinct fluctuation channel arises from quantum fluctuations of the magnetization itself. For a macrospin mode with magnon number $\dot{\Omega}_i=\sum_{j=1}^N H_{ij}\Omega_j,$9, the average magnon change per scattered electron is

$D=10$0

where the first term is spontaneous magnon emission enabled by zero-point magnetization fluctuations. Balancing this against damping yields

$D=10$1

whose non-smooth piecewise-linear dependence near $D=10$2 is the paper’s hallmark of quantum spin transfer. In this formulation, angular momentum can be transferred not only by directional spin-polarized current but also by thermal motion of electrons (Zholud et al., 2017).

A levitated ferromagnetic particle under microwave-driven FMR makes the stochastic Einstein–de Haas picture explicitly quantum. Spin relaxation is described by a Lindblad jump operator $D=10$3, each jump changes the spin angular momentum by $D=10$4, and the rigid body receives a mechanical increment $D=10$5. The fluctuating torque is

$D=10$6

and the resulting rotational noise spectrum contains a shot-noise term

$D=10$7

Because the mean rotation is

$D=10$8

the ratio

$D=10$9

plays the role of a rotational Fano factor. The paper further argues that a gyromagnetic bifurcation, where $d=1.5D$0, amplifies the rotational noise and can make the $d=1.5D$1-sized transfer quanta experimentally accessible (Sato et al., 2023).

5. Lattice, phonons, and internal angular-momentum redistribution

Within spin-lattice dynamics, fluctuation-induced angular-momentum transfer often appears as the excitation of internal vibrational modes rather than as immediate rigid-body rotation. In an Eckart-frame treatment of the Einstein–de Haas effect, the lattice angular momentum is decomposed into rigid-body, phonon-spin, phonon-orbital, and cross terms,

$d=1.5D$2

while the total transfer obeys

$d=1.5D$3

The key result is asymmetric partition: rigid-body rotation acquires the dominant share of angular momentum, while phonons absorb most of the resulting kinetic energy. Stronger pseudo-dipolar anisotropy increases the total amount of transferred angular momentum, whereas stronger Dzyaloshinskii–Moriya interaction accelerates the transfer rate and increases the proportion of phonon angular momentum (Nie et al., 28 Jan 2026).

A direct observation of angular-momentum transfer among lattice modes has now been reported in Bi$d=1.5D$4Se$d=1.5D$5. There, a circularly driven $d=1.5D$6 phonon at $d=1.5D$7 THz transfers angular momentum to an $d=1.5D$8 phonon at $d=1.5D$9 THz through the cubic anharmonic coupling $\lambda_1\sim -10^{-6}\,\mathrm{s}^{-1}$0, with the selection rule

$\lambda_1\sim -10^{-6}\,\mathrm{s}^{-1}$1

For the $\lambda_1\sim -10^{-6}\,\mathrm{s}^{-1}$2-symmetric crystal the process is a rotational phonon-phonon Umklapp event, $\lambda_1\sim -10^{-6}\,\mathrm{s}^{-1}$3, and in the circular basis the nonlinear force reads

$\lambda_1\sim -10^{-6}\,\mathrm{s}^{-1}$4

Experimentally the $\lambda_1\sim -10^{-6}\,\mathrm{s}^{-1}$5 mode exhibits a phase difference of exactly $\lambda_1\sim -10^{-6}\,\mathrm{s}^{-1}$6, approximately 3% of the absolute angular momentum of the $\lambda_1\sim -10^{-6}\,\mathrm{s}^{-1}$7 mode is transferred to the $\lambda_1\sim -10^{-6}\,\mathrm{s}^{-1}$8 mode, and the phononic pathway transfers three orders of magnitude more angular momentum than the direct photonic THz sum-frequency pathway (Minakova et al., 14 Mar 2025).

Even when every phonon mode has zero mean angular momentum, the phonon vacuum of a $\lambda_1\sim -10^{-6}\,\mathrm{s}^{-1}$9- and $1\,\mathrm{s}^{-1}$0-symmetric crystal can still possess finite angular-momentum fluctuations. The lattice angular momentum operator contains off-diagonal number-nonconserving terms,

$1\,\mathrm{s}^{-1}$1

and the relevant vacuum response is the retarded susceptibility

$1\,\mathrm{s}^{-1}$2

The resulting spectral weight sits at two-phonon sum frequencies and vanishes in the degenerate limit, so the effect is traced to coherence between nondegenerate, orthogonally polarized modes rather than to a nonzero static phonon chirality (Yi et al., 26 Jun 2025).

Hybrid bosonic transfer across separated solids has also been observed electrically in metallic ferromagnets. Two parallel, electrically insulated ferromagnetic strips on a diamagnetic substrate exhibit a finite nonlocal signal over micron distances, interpreted as angular momentum transfer from one strip to the other through either phononic or dipolar interactions. The transfer efficiency is fitted by

$1\,\mathrm{s}^{-1}$3

with $1\,\mathrm{s}^{-1}$4, while an alternative exponential fit gives $1\,\mathrm{s}^{-1}$5 for one Py-Py dataset. The signal scales approximately as $1\,\mathrm{s}^{-1}$6, disappears below about $1\,\mathrm{s}^{-1}$7, and is removed when one ferromagnet is replaced by Pt, indicating the importance of magnonic and thermally populated bosonic channels (Schlitz et al., 2023).

6. Turbulent, gauge-field, and statistical transport regimes

In several fields the fluctuating carrier is neither a photon nor a quasiparticle but a random stress or a fluctuating gauge field. For heavy quarks propagating through the evolving Glasma, the average angular momentum is set to zero, yet the anisotropic background fields generate anisotropic momentum broadening and hence anisotropic orbital-angular-momentum fluctuations. The paper defines

$1\,\mathrm{s}^{-1}$8

and finds $1\,\mathrm{s}^{-1}$9 of about 40% for $$n_g(\omega,q_x)=\frac{1}{e^{\hbar(\omega-q_x v_d)/k_B T_e}-1},$$0 fm and as large as 60% for $$n_g(\omega,q_x)=\frac{1}{e^{\hbar(\omega-q_x v_d)/k_B T_e}-1},$$1 fm over early-time windows up to $$n_g(\omega,q_x)=\frac{1}{e^{\hbar(\omega-q_x v_d)/k_B T_e}-1},$$2 fm/c. In the nonrelativistic toy-mass regime studied, spin fluctuations remain small and nearly isotropic, so the total-angular-momentum fluctuations are effectively orbital (Pooja et al., 2022).

A related but distinct mechanism appears in the early Glasma stage of noncentral nuclear collisions. There the angular momentum transferred to midrapidity is carried at early times by the rapidity-odd $$n_g(\omega,q_x)=\frac{1}{e^{\hbar(\omega-q_x v_d)/k_B T_e}-1},$$3-type flow,

$$n_g(\omega,q_x)=\frac{1}{e^{\hbar(\omega-q_x v_d)/k_B T_e}-1},$$4

which emerges from Gauss’ law for classical gluon fields. The resulting reaction-plane angular momentum per rapidity at $$n_g(\omega,q_x)=\frac{1}{e^{\hbar(\omega-q_x v_d)/k_B T_e}-1},$$5 is estimated as

$$n_g(\omega,q_x)=\frac{1}{e^{\hbar(\omega-q_x v_d)/k_B T_e}-1},$$6

at midrapidity. The paper further shows that this result reflects a cancellation between a vortex of energy flow aligned with the total angular momentum and an opposed longitudinal shear flow, and argues that dissipative corrections must be retained when matching the Yang–Mills tensor to fluid dynamics (Fries et al., 2017).

In laboratory liquid metals, angular-momentum transport by turbulence has been isolated experimentally in a thin-disk Galinstan apparatus driven by a volume Lorentz force. The local angular-momentum current is

$n_g(\omega,q_x)=\frac{1}{e^{\hbar(\omega-q_x v_d)/k_B T_e}-1},$7

and Reynolds decomposition separates it into a mean poloidal recirculation term and a fluctuation-only term,

$$n_g(\omega,q_x)=\frac{1}{e^{\hbar(\omega-q_x v_d)/k_B T_e}-1},$$8

Once the mean-advection contribution is subtracted, the turbulent transport follows

$$n_g(\omega,q_x)=\frac{1}{e^{\hbar(\omega-q_x v_d)/k_B T_e}-1},$$9

indicating a viscosity-independent ultimate regime of bulk fluctuation transport in a flow with $$m_y(\omega)= -\hbar \,\mathrm{Im}[\alpha(\omega)] \int\frac{d^2\mathbf q}{(2\pi)^2} q_x\,\mathrm{Im}\!\big(r_p e^{2i\beta_0 d}\big)\, \delta n(\omega,q_x),$$0 (Vernet et al., 2022).

Bounded 2D MHD turbulence provides another route in which random fields generate large-scale rotation only through boundary-mediated symmetry breaking. The exact balance for the kinetic angular momentum is

$$m_y(\omega)= -\hbar \,\mathrm{Im}[\alpha(\omega)] \int\frac{d^2\mathbf q}{(2\pi)^2} q_x\,\mathrm{Im}\!\big(r_p e^{2i\beta_0 d}\big)\, \delta n(\omega,q_x),$$1

In nonaxisymmetric domains such as a square, the pressure term is nonzero and rapid angular-momentum generation occurs; in axisymmetric domains such as a circle, it vanishes by symmetry and spontaneous spin-up is absent. Increasing the initial magnetic fluctuation level from $$m_y(\omega)= -\hbar \,\mathrm{Im}[\alpha(\omega)] \int\frac{d^2\mathbf q}{(2\pi)^2} q_x\,\mathrm{Im}\!\big(r_p e^{2i\beta_0 d}\big)\, \delta n(\omega,q_x),$$2 to $$m_y(\omega)= -\hbar \,\mathrm{Im}[\alpha(\omega)] \int\frac{d^2\mathbf q}{(2\pi)^2} q_x\,\mathrm{Im}\!\big(r_p e^{2i\beta_0 d}\big)\, \delta n(\omega,q_x),$$3 and $$m_y(\omega)= -\hbar \,\mathrm{Im}[\alpha(\omega)] \int\frac{d^2\mathbf q}{(2\pi)^2} q_x\,\mathrm{Im}\!\big(r_p e^{2i\beta_0 d}\big)\, \delta n(\omega,q_x),$$4 strengthens the square-domain spin-up, which the paper attributes to the magnetic-pressure contribution in $$m_y(\omega)= -\hbar \,\mathrm{Im}[\alpha(\omega)] \int\frac{d^2\mathbf q}{(2\pi)^2} q_x\,\mathrm{Im}\!\big(r_p e^{2i\beta_0 d}\big)\, \delta n(\omega,q_x),$$5 (Bos et al., 2010).

At heliophysical scales, Reynolds-averaged mean-field MHD shows that turbulence modifies the classic Weber–Davis angular-momentum loss of the solar wind by an $$m_y(\omega)= -\hbar \,\mathrm{Im}[\alpha(\omega)] \int\frac{d^2\mathbf q}{(2\pi)^2} q_x\,\mathrm{Im}\!\big(r_p e^{2i\beta_0 d}\big)\, \delta n(\omega,q_x),$$6 stress term,

$$m_y(\omega)= -\hbar \,\mathrm{Im}[\alpha(\omega)] \int\frac{d^2\mathbf q}{(2\pi)^2} q_x\,\mathrm{Im}\!\big(r_p e^{2i\beta_0 d}\big)\, \delta n(\omega,q_x),$$7

Using a turbulence-transport simulation and Parker Solar Probe data near the Alfvén surface, the paper finds $$m_y(\omega)= -\hbar \,\mathrm{Im}[\alpha(\omega)] \int\frac{d^2\mathbf q}{(2\pi)^2} q_x\,\mathrm{Im}\!\big(r_p e^{2i\beta_0 d}\big)\, \delta n(\omega,q_x),$$8 typically negative and of order $$m_y(\omega)= -\hbar \,\mathrm{Im}[\alpha(\omega)] \int\frac{d^2\mathbf q}{(2\pi)^2} q_x\,\mathrm{Im}\!\big(r_p e^{2i\beta_0 d}\big)\, \delta n(\omega,q_x),$$9–$i$00, with a simulation value $i$01 and an observational mean negative value $i$02. In this setting, turbulence reduces the effective angular-momentum loss rather than producing an additional outward channel of the same sign (Chhiber et al., 2 May 2025).

Turbulence also generates purely statistical orbital-angular-momentum fluctuations in wave propagation. For a spherical wave intercepted by a finite aperture after propagation through a random inhomogeneous medium, the mean OAM remains conserved but the aperture-averaged OAM fluctuates. The variance is governed by the fourth-order coherence function, depends strongly on aperture geometry, and the paper states that aperture averaging does not obey the standard “square root” law. It also emphasizes that the weak and strong fluctuation conditions for this aperture-averaged OAM are not defined by the values of the scintillation index of the incident wave (Charnotskii, 2018).