pith. sign in

arxiv: 2605.23197 · v2 · pith:4JM5JHDUnew · submitted 2026-05-22 · 🪐 quant-ph · gr-qc

Anomalous Decay of Quantum Resources: The Entanglement Sudden Death Mpemba Effect

Zhilong Liu , Zehua Tian , Jieci Wang This is my paper

Pith reviewed 2026-06-30 16:30 UTC · model grok-4.3

classification 🪐 quant-ph gr-qc
keywords quantum Mpemba effectentanglement sudden deathamplitude dampingopen quantum systemstwo-qubit entanglementquantum correlationsdissipative dynamics
0
0 comments X

The pith

More strongly entangled qubit pairs can reach separability sooner than weaker ones under amplitude damping.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines two qubits coupled to independent local amplitude-damping reservoirs and finds that certain initial states with greater entanglement become separable faster than states with lesser entanglement. The reversal occurs because higher excited-state population in the more entangled state accelerates the sudden death of entanglement enough to overcome its initial coherence advantage. Exact analytic expressions are derived for the time at which the entanglement trajectories cross and for the finite time at which entanglement vanishes. The authors also construct the phase diagram that locates the region of initial parameters where this ordering reversal appears. A reader would care because the result shows that the lifetime of quantum correlations in noise is controlled by a competition between coherence and population rather than by entanglement strength alone.

Core claim

In two-qubit systems evolving under independent local amplitude-damping channels, there exist pairs of initial states belonging to a two-parameter family such that the state with larger initial entanglement reaches a separable state in shorter time than the state with smaller initial entanglement. The anomalous ordering is produced by the competition in which the difference in excited-state population acts as a catalyst that can dominate the protective effect of initial coherence, yielding an exact crossover time before both states undergo entanglement sudden death.

What carries the argument

The two-parameter family of initial states together with the analytic crossover condition on concurrence (or negativity) under identical local amplitude-damping channels.

If this is right

  • Entanglement lifetime can be lengthened or shortened by tuning initial population at fixed entanglement.
  • A phase diagram in the initial-state parameter space separates the normal decay regime from the anomalous Mpemba regime.
  • Closed-form expressions give the precise entanglement sudden death time for every member of the two-parameter family.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Population engineering could serve as an additional control knob for protecting or destroying quantum correlations in open-system protocols.
  • Analogous reversal effects may appear for other resource measures such as coherence or discord under the same noise model.
  • The phenomenon invites checking whether unequal damping rates or added dephasing terms preserve or destroy the crossover.

Load-bearing premise

The qubits evolve under identical independent local amplitude-damping channels and the initial states belong to a two-parameter family in which entanglement and excited-state population can be varied separately.

What would settle it

Direct computation or laboratory measurement of the entanglement measure as a function of time for two concrete initial states, one more entangled but carrying higher excited population, to check whether that state reaches zero entanglement earlier than the less entangled state.

Figures

Figures reproduced from arXiv: 2605.23197 by Jieci Wang, Zehua Tian, Zhilong Liu.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic representation of the dissipative model. A bipar [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Decay of concurrence under symmetric dissipation [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Phase diagrams: solid black semicircle is physical boundary [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Characteristic timescales and their dimensionless ratios vary [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
read the original abstract

In classical thermodynamics, the Mpemba effect refers to the counterintuitive observation that hot water can freeze faster than cold water, manifesting as an anomalous crossing of dynamical trajectories. While analogues of this phenomenon have been explored in open quantum systems and spin-chain entanglement asymmetry, its connection to the finite-time decoupling of quantum correlations remains elusive. In this Letter, we uncover a distinct quantum Mpemba effect associated with entanglement sudden death (ESD). By analyzing two qubits interacting with local amplitude damping reservoirs, we demonstrate that a more strongly entangled initial state can experience a faster collapse into a separable state than a more weakly entangled one. This anomalous decay stems from the competition between initial coherence and excited-state population, where the latter acts as a catalyst for entanglement sudden death. We provide exact analytical derivations for the trajectory crossover and ESD time, and map the phase diagram to precisely identify the parameter regime where the effect occurs. Our results offer a new strategy for controlling the lifetime of quantum resources in dissipative environments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript claims that two qubits undergoing independent local amplitude-damping channels exhibit an entanglement sudden death (ESD) Mpemba effect: for initial states drawn from a two-parameter family, a more strongly entangled state can reach separability faster than a less entangled one because the excited-state population acts as a catalyst. Exact analytical expressions are derived for the entanglement-trajectory crossover time and the ESD time, and a phase diagram is constructed to delineate the parameter regime in which the anomalous ordering occurs.

Significance. The provision of exact analytical derivations for the crossover and ESD times, together with the explicit phase diagram, is a clear strength that permits direct verification of the claimed effect without numerical fitting. If the central claim holds under the stated model (equal-rate local amplitude damping and the indicated initial-state family), the work supplies a concrete strategy for controlling the lifetime of quantum resources by tuning the competition between coherence and population.

minor comments (2)
  1. [Abstract] Abstract: the two-parameter initial-state family is referenced but the angle that controls entanglement versus excited-state population is not named; adding the explicit parametrization would improve immediate readability.
  2. The manuscript would benefit from a brief statement confirming that the reported crossover and ESD times remain valid when the two damping rates differ by a small amount, even if the main analysis assumes equality.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript, the recognition of the exact analytical derivations and phase diagram as strengths, and the recommendation for minor revision. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper derives the entanglement sudden death times and trajectory crossovers analytically from the standard two-qubit amplitude damping master equation applied to a two-parameter family of initial states. The central claim of the Mpemba-like effect arises directly from comparing these exact expressions for different initial entanglement and population parameters, without reduction to fitted quantities or self-citations. The derivations rest on the independent local damping channels and do not invoke uniqueness theorems or ansatze from prior self-work in a load-bearing way.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard Markovian amplitude-damping model and a two-parameter family of initial states; no new entities are postulated.

free parameters (2)
  • initial-state angle
    Parameter controlling the degree of entanglement and excited-state population in the chosen initial-state family.
  • damping rate gamma
    Amplitude-damping rate assumed identical for both local reservoirs.
axioms (1)
  • domain assumption The joint evolution obeys the Markovian master equation for independent local amplitude-damping channels
    Standard model for spontaneous emission; invoked to obtain the time-dependent density matrix.

pith-pipeline@v0.9.1-grok · 5700 in / 1279 out tokens · 39116 ms · 2026-06-30T16:30:03.048175+00:00 · methodology

Review history (2 revisions) →

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

60 extracted references · 52 canonical work pages · 10 internal anchors

  1. [1]

    E. B. Mpemba and D. G. Osborne, Cool?, Phys. Educ.4, 172 (1969)

    1969

  2. [2]

    Lu and O

    Z. Lu and O. Raz, Nonequilibrium thermodynamics of the markovian mpemba effect and its inverse, Proc. Natl. Acad. Sci. U.S.A.114, 5083 (2017)

    2017

  3. [3]

    Beato and G

    N. Beato and G. Teza, Relaxation Control of Open Quantum Systems, Phys. Rev. Lett.136, 070401 (2026), arXiv:2507.15948 [quant-ph]

    work page arXiv 2026

  4. [4]

    Bao, Initial-State Typicality in Quantum Relaxation, Phys

    R. Bao, Initial-State Typicality in Quantum Relaxation, Phys. Rev. Lett.136, 070402 (2026), arXiv:2511.01709 [quant-ph]

    work page arXiv 2026

  5. [5]

    Nava and R

    A. Nava and R. Egger, Pontus-Mpemba Effects, Phys. Rev. Lett. 135, 140404 (2025), arXiv:2505.14622 [quant-ph]

    work page arXiv 2025

  6. [6]

    Carollo, A

    F. Carollo, A. Lasanta, and I. Lesanovsky, Exponentially accel- erated approach to stationarity in Markovian open quantum sys- tems through the Mpemba effect, Phys. Rev. Lett.127, 060401 (2021), arXiv:2103.05020 [quant-ph]

    work page arXiv 2021

  7. [7]

    Longhi, Photonic Mpemba effect, Opt

    S. Longhi, Photonic Mpemba effect, Opt. Lett.49, 5188 (2024), arXiv:2408.03296 [physics.optics]

    work page arXiv 2024

  8. [8]

    Van Vu and H

    T. Van Vu and H. Hayakawa, Thermomajorization Mpemba Effect, Phys. Rev. Lett.134, 107101 (2025), arXiv:2410.06686 [cond-mat.stat-mech]

    work page arXiv 2025

  9. [9]

    Bao and Z

    R. Bao and Z. Hou, Accelerating Quantum Relaxation via Tem- porary Reset: A Mpemba-Inspired Approach, Phys. Rev. Lett. 135, 150403 (2025), arXiv:2212.11170 [quant-ph]

    work page arXiv 2025

  10. [10]

    Wang and J

    X. Wang and J. Wang, Mpemba effects in nonequilibrium open quantum systems, Phys. Rev. Res.6, 033330 (2024), arXiv:2401.14259 [quant-ph]

    work page arXiv 2024

  11. [11]

    D. J. Strachan, A. Purkayastha, and S. R. Clark, Non-Markovian Quantum Mpemba Effect, Phys. Rev. Lett.134, 220403 (2025), arXiv:2402.05756 [quant-ph]

    work page arXiv 2025

  12. [12]

    Moroder, O

    M. Moroder, O. Culhane, K. Zawadzki, and J. Goold, Thermo- dynamics of the Quantum Mpemba Effect, Phys. Rev. Lett.133, 140404 (2024), arXiv:2403.16959 [quant-ph]

    work page arXiv 2024

  13. [13]

    A. K. Chatterjee, S. Takada, and H. Hayakawa, Quantum Mpemba Effect in a Quantum Dot with Reservoirs, Phys. Rev. Lett.131, 080402 (2023), arXiv:2304.02411 [cond-mat.stat- mech]

    work page arXiv 2023

  14. [14]

    Torrente, M

    A. Torrente, M. A. L ´opez-Casta˜no, A. Lasanta, F. V . Reyes, A. Prados, and A. Santos, Large mpemba-like effect in a gas of inelastic rough hard spheres, Phys. Rev. E99, 060901(R) (2019)

    2019

  15. [15]

    Kumar and J

    A. Kumar and J. Bechhoefer, Exponentially faster cooling in a colloidal system, Nature584, 64 (2020)

    2020

  16. [16]

    Aharony Shapira, Y

    S. Aharony Shapira, Y . Shapira, J. Markov, G. Teza, N. Akerman, O. Raz, and R. Ozeri, Inverse Mpemba Effect Demonstrated on a Single Trapped Ion Qubit, Phys. Rev. Lett.133, 010403 (2024), arXiv:2401.05830 [quant-ph]

    work page arXiv 2024

  17. [17]

    Zhanget al., Observation of quantum strong Mpemba effect, Nature Commun.16, 301 (2025), arXiv:2401.15951 [quant-ph]

    J. Zhanget al., Observation of quantum strong Mpemba effect, Nature Commun.16, 301 (2025), arXiv:2401.15951 [quant-ph]

    work page arXiv 2025

  18. [18]

    F. Ares, P. Calabrese, and S. Murciano, The quantum Mpemba ef- fects, Nature Rev. Phys.7, 451 (2025), arXiv:2502.08087 [cond- mat.stat-mech]

    work page arXiv 2025

  19. [19]

    G. Teza, J. Bechhoefer, A. Lasanta, O. Raz, and M. Vucelja, Speedups in nonequilibrium thermal relaxation: Mpemba and related effects, Phys. Rept.1164, 1 (2026), arXiv:2502.01758 [cond-mat.stat-mech]

    work page arXiv 2026

  20. [20]

    Bechhoefer, A

    J. Bechhoefer, A. Kumar, and R. Ch´etrite, A fresh understanding of the mpemba effect, Nat. Rev. Phys.3, 534 (2021)

    2021

  21. [21]

    H. Yu, S. Liu, and S.-X. Zhang, Quantum Mpemba effects from symmetry perspectives, AAPPS Bull.35, 17 (2025), arXiv:2507.02301 [quant-ph]

    work page arXiv 2025

  22. [22]

    Chang, S

    W.-X. Chang, S. Yin, S.-X. Zhang, and Z.-X. Li, Imaginary-Time Mpemba Effect in Quantum Many-Body Systems, Phys. Rev. Lett.136, 100403 (2026), arXiv:2409.06547 [cond-mat.str-el]

    work page arXiv 2026

  23. [23]

    H. Yu, J. Hu, and S.-X. Zhang, Quantum pontus-Mpemba effects in real- and imaginary-time dynamics, Phys. Rev. B113, 134304 (2026), arXiv:2509.01960 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  24. [24]

    F. Ares, S. Murciano, and P. Calabrese, Entanglement asymmetry as a probe of symmetry breaking, Nature Commun.14, 2036 (2023), arXiv:2207.14693 [cond-mat.stat-mech]

    work page arXiv 2036

  25. [25]

    Yu, Z.-X

    H. Yu, Z.-X. Li, and S.-X. Zhang, Symmetry Breaking Dynamics in Quantum Many-Body Systems, Chin. Phys. Lett.42, 110602 (2025), arXiv:2501.13459 [quant-ph]

    work page arXiv 2025

  26. [26]

    Klobas, C

    K. Klobas, C. Rylands, and B. Bertini, Translation symmetry restoration under random unitary dynamics, Phys. Rev. B111, L140304 (2025), arXiv:2406.04296 [cond-mat.stat-mech]

    work page arXiv 2025

  27. [27]

    Summer, M

    A. Summer, M. Moroder, L. P. Bettmann, X. Turkeshi, I. Mar- vian, and J. Goold, Resource-Theoretical Unification of Mpemba Effects: Classical and Quantum, Phys. Rev. X16, 011065 (2026), arXiv:2507.16976 [quant-ph]

    work page arXiv 2026

  28. [28]

    Liu, H.-K

    S. Liu, H.-K. Zhang, S. Yin, S.-X. Zhang, and H. Yao, Symmetry restoration and quantum Mpemba effect in many-body local- ization systems, Sci. Bull.70, 3991 (2025), arXiv:2408.07750 [cond-mat.dis-nn]

    work page arXiv 2025

  29. [29]

    Foligno, P

    A. Foligno, P. Calabrese, and B. Bertini, Nonequilibrium Dynam- ics of Charged Dual-Unitary Circuits, PRX Quantum6, 010324 (2025), arXiv:2407.21786 [cond-mat.stat-mech]

    work page arXiv 2025

  30. [30]

    Bertini, P

    B. Bertini, P. Calabrese, M. Collura, K. Klobas, and C. Ry- lands, Nonequilibrium Full Counting Statistics and Symmetry- Resolved Entanglement from Space-Time Duality, Phys. Rev. Lett.131, 140401 (2023), arXiv:2212.06188 [cond-mat.stat- mech]

    work page arXiv 2023

  31. [31]

    Yamashika, F

    S. Yamashika, F. Ares, and P. Calabrese, Entanglement asymme- 6 try and quantum Mpemba effect in two-dimensional free-fermion systems, Phys. Rev. B110, 085126 (2024), arXiv:2403.04486 [cond-mat.stat-mech]

    work page arXiv 2024

  32. [32]

    Murciano, F

    S. Murciano, F. Ares, I. Klich, and P. Calabrese, Entanglement asymmetry and quantum Mpemba effect in the XY spin chain, J. Stat. Mech.2401, 013103 (2024), arXiv:2310.07513 [cond- mat.stat-mech]

    work page arXiv 2024

  33. [33]

    Y . Yu, T. Jin, L. Zhang, K. Xu, and H. Fan, Tuning the quantum Mpemba effect in an isolated system by initial-state engineering, Phys. Rev. B112, 094315 (2025), arXiv:2505.02040 [quant-ph]

    work page arXiv 2025

  34. [34]

    Rylands, K

    C. Rylands, K. Klobas, F. Ares, P. Calabrese, S. Murciano, and B. Bertini, Microscopic Origin of the Quantum Mpemba Effect in Integrable Systems, Phys. Rev. Lett.133, 010401 (2024), arXiv:2310.04419 [cond-mat.stat-mech]

    work page arXiv 2024

  35. [35]

    Observation and Modulation of the Quantum Mpemba Effect on a Superconducting Quantum Processor

    Y . Xuet al., Observation and Modulation of the Quantum Mpemba Effect on a Superconducting Quantum Processor, (2025), arXiv:2508.07707 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  36. [36]

    A. Rath, V . Vitale, S. Murciano, M. V otto, J. Dubail, R. Kueng, C. Branciard, P. Calabrese, and B. Vermersch, Entanglement Bar- rier and its Symmetry Resolution: Theory and Experimental Ob- servation, PRX Quantum4, 010318 (2023), arXiv:2209.04393 [quant-ph]

    work page arXiv 2023

  37. [37]

    L. K. Joshiet al., Observing the Quantum Mpemba Effect in Quantum Simulations, Phys. Rev. Lett.133, 010402 (2024), arXiv:2401.04270 [quant-ph]

    work page arXiv 2024

  38. [38]

    Turkeshi, P

    X. Turkeshi, P. Calabrese, and A. De Luca, Quantum Mpemba Effect in Random Circuits, Phys. Rev. Lett.135, 040403 (2025), arXiv:2405.14514 [quant-ph]

    work page arXiv 2025

  39. [39]

    Liu, H.-K

    S. Liu, H.-K. Zhang, S. Yin, and S.-X. Zhang, Symmetry Restora- tion and Quantum Mpemba Effect in Symmetric Random Cir- cuits, Phys. Rev. Lett.133, 140405 (2024), arXiv:2403.08459 [quant-ph]

    work page arXiv 2024

  40. [40]

    Yamashika and F

    S. Yamashika and F. Ares, Quantum Mpemba Effect in Long- Range Spin Systems, Phys. Rev. Lett.136, 090402 (2026), arXiv:2507.06636 [cond-mat.stat-mech]

    work page arXiv 2026

  41. [41]

    Medina, O

    I. Medina, O. Culhane, F. C. Binder, G. T. Landi, and J. Goold, Anomalous Discharging of Quantum Batteries: The Ergotropic Mpemba Effect, Phys. Rev. Lett.134, 220402 (2025), arXiv:2412.13259 [quant-ph]

    work page arXiv 2025

  42. [42]

    Sapui, T

    T. Sapui, T. K. Konar, and A. S. De, Ergotropic Mpemba crossings in finite-dimensional quantum batteries, (2026), arXiv:2602.11056 [quant-ph]

    work page arXiv 2026

  43. [43]

    Y . Li, W. Li, and X. Li, Ergotropic mpemba effect in non- markovian quantum systems, Phys. Rev. A112, 032209 (2025)

    2025

  44. [44]

    Yu and J

    T. Yu and J. H. Eberly, Sudden death of entanglement: Classi- cal noise effects, Opt. Commun.264, 393 (2006), arXiv:quant- ph/0602196

    work page arXiv 2006

  45. [45]

    Finite-Time Disentanglement via Spontaneous Emission

    T. Yu and J. H. Eberly, Finite-Time Disentanglement Via Spontaneous Emission, Phys. Rev. Lett.93, 140404 (2004), arXiv:quant-ph/0404161

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  46. [46]

    M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Wal- born, P. H. S. Ribeiro, and L. Davidovich, Environment-Induced Sudden Death of Entanglement, Science316, 1139892 (2007), arXiv:quant-ph/0701184

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  47. [47]

    Li, S.-H

    S.-H. Li, S.-H. Shang, and S.-M. Wu, Does acceleration always degrade quantum entanglement for tetrapartite Unruh-DeWitt detectors?, JHEP05, 214, arXiv:2502.05881 [gr-qc]

    work page arXiv

  48. [48]

    X. Liu, W. Liu, and S.-M. Wu, Entanglement degradation of static black holes in effective quantum gravity, Phys. Lett. B875, 140334 (2026), arXiv:2511.12245 [gr-qc]

    work page arXiv 2026

  49. [49]

    Gallock-Yoshimura and R

    K. Gallock-Yoshimura and R. B. Mann, Entangled detectors nonperturbatively harvest mutual information, Phys. Rev. D104, 125017 (2021), arXiv:2109.07495 [quant-ph]

    work page arXiv 2021

  50. [50]

    Entanglement dynamics of two independent qubits in environments with and without memory

    B. Bellomo, R. L. Franco, and G. Compagno, Entanglement dy- namics of two independent qubits in environments with and with- out memory, Phys. Rev. A77, 032342 (2008), arXiv:0711.4799 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  51. [51]

    Non-Markovian effects on the dynamics of entanglement

    B. Bellomo, R. L. Franco, and G. Compagno, Non-Markovian Effects on the Dynamics of Entanglement, Phys. Rev. Lett.99, 160502 (2007), arXiv:0804.2377 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  52. [52]

    Y . Pan, B. Zhang, and Q. Cai, Entanglement is protected by acceleration-induced transparency in thermal field, Phys. Rev. D 113, 025004 (2026), arXiv:2512.06043 [quant-ph]

    work page arXiv 2026

  53. [53]

    M. F. Cavalcante, M. V . S. Bonanc ¸a, E. Miranda, and S. Deffner, Emergence of X states in a quantum impurity model, Phys. Rev. Res.7, L022027 (2025), arXiv:2501.13914 [cond-mat.str-el]

    work page arXiv 2025

  54. [54]

    Entanglement dynamics and performance of two-qubit gates for superconducting qubits under non-Markovian effects

    K. Nakamura and J. Ankerhold, Entanglement dynamics and performance of two-qubit gates for superconducting qubits un- der non-Markovian effects, Phys. Rev. Res.8, 013337 (2026), arXiv:2510.05872 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  55. [55]

    A. R. P. Rau, Algebraic characterization of X-states in quantum information, J. Phys. A42, 412002 (2009), arXiv:0906.4716 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  56. [56]

    Evolution from Entanglement to Decoherence of Bipartite Mixed "X" States

    T. Yu and J. H. Eberly, Evolution from entanglement to decoher- ence of bipartite mixed ”X” states, Quant. Inf. Comput.7, 459 (2007), arXiv:quant-ph/0503089

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  57. [57]

    Entanglement of a Pair of Quantum Bits

    S. Hill and W. K. Wootters, Entanglement of a pair of quantum bits, Phys. Rev. Lett.78, 5022 (1997), arXiv:quant-ph/9703041

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  58. [58]

    W. K. Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett.80, 2245 (1998), arXiv:quant- ph/9709029

    work page arXiv 1998

  59. [59]

    Klich, O

    I. Klich, O. Raz, O. Hirschberg, and M. Vucelja, Mpemba index and anomalous relaxation, Phys. Rev. X9, 021060 (2019)

    2019

  60. [60]

    Kumar, R

    A. Kumar, R. Ch ´etrite, and J. Bechhoefer, Anomalous heat- ing in a colloidal system, Proc. Natl. Acad. Sci. U.S.A.119, e2118484119 (2022). Appendix In this Appendix, we provide the explicit derivation steps for the asymmetric dissipation framework and present supple- mentary analysis regarding the geometric boundaries of the phase diagrams. WhenΓ A , ΓB...

    2022