Chirality-Dependent Effective Temperature

• Chirality-dependent effective temperature is an umbrella concept describing how chiral systems exhibit distinct thermal responses without defining independent left- or right-handed temperatures.
• Key studies demonstrate that temperature-dependent anomalies can alter transport coefficients and excitation dynamics via linear or quadratic scaling with temperature.
• Experimental and theoretical findings reveal that chiral optical, phononic, and magnetic systems experience enhanced and asymmetric responses under common thermal drives.

Searching arXiv for recent and relevant papers on chirality and temperature dependence. Searching arXiv for "chirality temperature dependence effective temperature chiral anomaly phonon CISS". Chirality-dependent effective temperature is not a single, uniformly defined concept across current research literatures. Taken together, the relevant works suggest an umbrella usage for several distinct phenomena: temperature-dependent anomalous chiral response in quantum field theory, chirality-resolved thermal averages of chiral excitations, chirality-dependent transport coefficients under a common thermal drive, and genuine helicity-dependent steady-state temperature differences in chiral photothermal systems. Several of the most relevant papers explicitly state that they do not introduce separate left- and right-handed temperatures; instead, chirality modifies how a system responds to the ordinary temperature $T$, or how opposite helicities generate different measured temperatures (Das et al., 2010, Huang et al., 11 Apr 2026, Dey et al., 2022, Schnoering et al., 2020, Mohammadi et al., 2024).

1. Terminological status and scope

In the strict thermodynamic sense, a chirality-dependent effective temperature would mean distinct temperatures assigned to different chiral sectors, such as left- and right-handed fermions, or to positive- and negative-helicity excitations. The literature surveyed here rarely adopts that construction. In the finite-temperature Schwinger model, temperature remains a single bath parameter $T$, and the effect is a thermal anomaly functional rather than a chirality-resolved thermal state (Das et al., 2010). In the phonon-chirality framework, the Bose-Einstein occupation factor depends only on $\omega$ and the common bath temperature $T$, not on chirality, so there is no explicit population imbalance between opposite-handed phonons generated by thermal equilibrium alone (Huang et al., 11 Apr 2026).

A closely related but distinct usage appears in transport theory. In weakly magnetized thermal QCD, the same temperature gradient acts on both chiral sectors, but left- and right-handed quasifermion modes acquire different effective masses and therefore different Seebeck and Nernst responses (Dey et al., 2022). In stochastic optomechanics, the bath temperature remains the ordinary $T$, with $D=k_B T/\gamma$, while chirality enters through reactive or dissipative optical forces that bias barrier crossing and stationary populations (Schnoering et al., 2020). The nearest literal temperature asymmetry occurs in thermal circular dichroism, where the central observable is the real steady-state temperature difference

$\mathrm{TCD}=T_R-T_L,$

with $T_R$ and $T_L$ measured under right- and left-circularly polarized excitation, respectively (Mohammadi et al., 2024).

This distribution of meanings is central to the subject. A useful synthesis is that the phrase most often denotes chirality-dependent thermal response rather than a new thermodynamic state variable.

2. Finite-temperature anomalies and chiral vortical transport

In relativistic field theory, the most direct connections between chirality and temperature arise in anomalous transport and anomalous current nonconservation. In the $1+1$-dimensional Schwinger model, finite temperature does not modify the usual ultraviolet chiral anomaly, because temperature-dependent parts of amplitudes are UV finite. The paper instead demonstrates a distinct, temperature-dependent anomaly of infrared origin, generated when the external electric field has nontrivial long-distance behavior. In the high-temperature limit the relevant coefficient is linear in $T$0, and the effect extends beyond the two-point function to all even-point amplitudes (Das et al., 2010).

A related but different construction appears in early-universe chiral magnetohydrodynamics. There the chiral vortical current is written with an additional temperature-dependent term for hotter or colder nonthermal species,

$T$1

so the vortical coefficient becomes

$T$2

This does not define $T$3 and $T$4; rather, it adds a temperature-dependent correction to anomalous vortical transport in a chirally imbalanced plasma. Numerically, the large-scale magnetic spectrum remains unchanged, while in the Kolmogorov regime the peak becomes negatively skewed and is fit by a beta distribution (Mukherjee et al., 2017).

The temperature dependence of the axial vortical effect is itself not universal. For the axial current coefficient

$T$5

the $T$6 term is argued to be model dependent rather than generally fixed by the mixed gauge-gravitational anomaly. In a low-temperature pionic or chiral-superfluid regime, the thermal correction is

$T$7

whereas in the high-temperature free-fermion regime one finds

$T$8

The sign and structure of the temperature correction therefore depend on the active chiral degrees of freedom and on their statistics (Kalaydzhyan, 2014).

These field-theoretic results support a precise conclusion: finite temperature can modify anomalous chiral response, sometimes linearly in $T$9, sometimes through $\omega$0, but this is not equivalent to assigning separate effective temperatures to opposite chiralities.

3. Chiral excitations, thermal occupation, and excitation-specific thermal scales

In lattice dynamics, phonon chirality provides one of the clearest equilibrium frameworks for a chirality-sensitive thermal average. The microscopic quantity is the phonon angular momentum $\omega$1, whose projection onto the propagation direction defines a momentum-resolved dynamical chirality, written in the supplemental text as

$\omega$2

Bulk dynamical chirality is then constructed from symmetry-weighted Brillouin-zone sums,

$\omega$3

and

$\omega$4

Temperature enters explicitly and only through the Bose-Einstein factor

$\omega$5

and at high temperature both $\omega$6 and $\omega$7 scale approximately linearly with $\omega$8. The intrinsic handedness of each mode is unchanged; temperature changes the bulk magnitude through thermal occupation (Huang et al., 11 Apr 2026).

The same paper also sharpens the difference between local and bulk chirality. In chiral materials such as Se, Te, and $\omega$9-HgS, the momentum-resolved quantity is nonzero and reverses sign between left- and right-handed enantiomers. In centrosymmetric crystals it vanishes at all wave vectors. In noncentrosymmetric achiral crystals, local chirality can be finite but the Brillouin-zone sum vanishes, so the bulk dynamical chirality is zero (Huang et al., 11 Apr 2026). This is directly relevant to any effective-temperature interpretation, because a nonzero thermal average need not imply separate thermal sectors; it can instead reflect symmetry-structured mode populations under a common bath temperature.

A different equilibrium phenomenon appears in the spin-$T$0 zigzag $T$1 chain. There the local vector chirality is

$T$2

In the chiral phase, chiral long-range order present at $T$3 disappears at finite temperature. In the neighboring dimer phase, however, static chiral correlation and spin correlation increase with temperature, reach a maximum around

$T$4

and are associated with enhanced spectral weight inside a chiral gap of order

$T$5

The paper interprets this as evidence for chiral excited states above a nonchiral ground state (Sugimoto et al., 2010). A plausible implication is that some systems possess a chirality-specific thermal activation scale without possessing a chirality-specific temperature.

4. Chirality-dependent transport coefficients and crossover structure

In solid-state transport, chirality often enters through dispersion, overlap factors, or quasiparticle masses rather than through an independent thermal variable. For phonon-limited resistivity in graphene multilayers, the relevant temperature scale is the ordinary Bloch-Grüneisen temperature,

$T$6

No new temperature parameter is introduced. Chirality instead modifies the coefficients and density scalings of the high- and low-temperature laws through $T$7, $T$8, and the chiral overlap factor $T$9. In the unscreened case,

$T$0

at high temperature and

$T$1

in the low-temperature Bloch-Grüneisen regime. With screening,

$T$2

with a renormalized $T$3, while

$T$4

and $T$5 becomes independent of $T$6 (Min et al., 2010). The observed thermal behavior is therefore chirality dependent in amplitude and crossover structure, not in temperature definition.

Weakly magnetized thermal QCD yields a more explicitly chiral thermal response. The weak magnetic field lifts the degeneracy between left- and right-handed quasifermion modes, producing effective masses

$T$7

As a result, the thermoelectric tensor becomes chirality dependent. Both the diagonal Seebeck coefficient and the off-diagonal Hall-type Nernst coefficient are larger in the $T$8 mode than in the $T$9 mode, and the disparity is more pronounced in the Nernst coefficient. The paper reports a maximum relative difference of $D=k_B T/\gamma$0 for the Seebeck coefficient in the 2-D setup and $D=k_B T/\gamma$1 for the Nernst coefficient. It also reports that the Seebeck coefficient magnitude is significantly enhanced, by one order of magnitude, in the 2-D setup compared with a 1-D temperature profile (Dey et al., 2022).

Here again, the physical meaning is not $D=k_B T/\gamma$2. Both sectors are driven by the same thermal gradient, but their induced electric responses differ because the weak magnetic field generates chirality-dependent quasifermion spectra. This is a paradigmatic example of chirality-dependent thermal response without chirality-dependent thermodynamic temperature.

5. CISS, spin-selective interfaces, and anomalous thermal trends

The literature on the chirality-induced spin selectivity effect uses temperature primarily as a diagnostic of microscopic mechanism. A review centered on the spinterface scenario states that vibrational or phonon-based mechanisms generally predict that CISS strengthens as temperature rises, whereas non-vibrational mechanisms, especially the spinterface mechanism, predict that CISS is already finite at low $D=k_B T/\gamma$3 and is weakened by thermal fluctuations (Alwan et al., 2022). In the spinterface model,

$D=k_B T/\gamma$4

with

$D=k_B T/\gamma$5

so temperature enters through a competition between the interfacial effective field and the real thermal energy $D=k_B T/\gamma$6. The same paper is explicit that this is not an effective temperature formalism. Its reinterpretation of the Qian et al. data argues that the Arrhenius-normalized spin signal decreases monotonically with increasing temperature and that the data therefore support stronger CISS at lower temperature (Alwan et al., 2022).

A different thermal trend is reported for chirality-induced magnetization in a chiral molecule/magnetic surface system associated with CISS. In experiments with ribo-aminooxazoline (RAO) crystals on Ni/Au thin films, the local coercive field under the crystals is already about $D=k_B T/\gamma$7 higher than on the bare surface at room temperature, and this excess coercivity increases linearly with temperature over the measured range. At $D=k_B T/\gamma$8, all domains have flipped at $D=k_B T/\gamma$9, whereas some domains under the RAO crystals remain unflipped at $\mathrm{TCD}=T_R-T_L,$0. The Hall response also increases more strongly in the presence of RAO than on the bare substrate (Kapon et al., 2024). The paper characterizes this as a non-classical temperature dependence and interprets it as evidence for a phonon- or vibron-assisted contribution to CISS.

The same work proposes a phenomenological temperature-dependent magnon dispersion

$\mathrm{TCD}=T_R-T_L,$1

where the $\mathrm{TCD}=T_R-T_L,$2 term is interpreted as a linear-in-temperature enhancement of anisotropy arising from spin-lattice coupling in chiral structures (Kapon et al., 2024). This does not establish a chirality-dependent effective temperature, but it does establish chirality-enabled constructive coupling between thermal fluctuations and magnetic response. In the same study, the chemistry of RAO synthesis shows that the RAO/AAO ratio increases from $\mathrm{TCD}=T_R-T_L,$3 at $\mathrm{TCD}=T_R-T_L,$4 to $\mathrm{TCD}=T_R-T_L,$5 at $\mathrm{TCD}=T_R-T_L,$6, while RAO abundance rises from $\mathrm{TCD}=T_R-T_L,$7 to $\mathrm{TCD}=T_R-T_L,$8 (Kapon et al., 2024). The magnetic and chemical results are presented as parallel evidence that temperature can enhance rather than suppress some chirality-linked processes.

6. Actual differential temperatures, nonequilibrium analogies, and conceptual limits

Among the works most closely related to the literal wording of the topic, nanophotonic thermal circular dichroism is distinctive because it defines a real chirality-dependent temperature observable: $\mathrm{TCD}=T_R-T_L,$9 Here $T_R$0 and $T_R$1 are steady-state temperatures under right- and left-circularly polarized excitation. The temperature difference is linked to the differential absorbed power through

$T_R$2

and the central physical mechanisms are chirality transfer to dielectric Mie resonators and self-heating, with further amplification by collective thermal effects and optical lattice resonances in arrays. For a silicon sphere with a chiral shell, the paper reports $T_R$3 at $T_R$4 and $T_R$5, compared with $T_R$6 for the equivalent chiral sphere baseline, corresponding to an enhancement of about $T_R$7. In large 2D thermally coupled arrays, the predicted enhancement reaches $T_R$8, that is, more than 4 orders of magnitude (Mohammadi et al., 2024). This is not an effective temperature in the coarse-grained thermodynamic sense; it is an actual helicity-dependent steady-state temperature difference.

Stochastic thermodynamics in tailored chiral optical environments provides the most developed nonequilibrium analogue. An overdamped chiral nanoparticle diffusing in a standing-wave double well experiences either a conservative reactive chiral force, which modifies the Helmholtz free-energy landscape, or a non-conservative dissipative chiral force, which creates a nonequilibrium steady state with heat transfer and entropy production (Schnoering et al., 2020). In the reactive case, the barrier-crossing rates acquire chirality-dependent Arrhenius factors through an added potential $T_R$9. In the dissipative case, the escape-rate ratio becomes

$T_L$0

so chirality biases activated dynamics under the same bath temperature $T_L$1 (Schnoering et al., 2020). The paper is explicit that this is a nonequilibrium steady-state description, not a redefinition of temperature.

Taken together, these works suggest a sharp conceptual boundary. The phrase “chirality-dependent effective temperature” is best reserved, if used at all, for carefully delimited operational contexts such as $T_L$2 in thermal circular dichroism. In most of the literature, the technically correct description is different: finite temperature modifies anomalous chiral response, thermally populated chiral excitations generate nonzero bulk chirality, left- and right-handed quasiparticles exhibit different transport coefficients under a common thermal drive, and chirality-dependent forces bias nonequilibrium activation. The dominant research picture is therefore one of chirality-dependent thermal response, chirality-dependent thermal scales, or chirality-dependent nonequilibrium activation, rather than a universal chirality-resolved temperature.