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Frenesy (physics)

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Frenesy is a concept in statistical physics that measures the dynamical activity of a system's microscopic trajectories under non-equilibrium conditions.[1] It complements the notion of entropy production, which measures time-antisymmetric aspects associated with irreversibility. Frenesy reflects how frequently states are visited or how many transitions occur over time and how busy the system's trajectories are. It relates to reactivities, escape rates and residence times of a physical state.

Origin and context

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The notion of frenesy was introduced in 2006 in the study of non-equilibrium processes by Christian Maes and collaborators, and has been discussed in various studies since then.[2][3] In systems described by trajectory ensembles or path-space measures (e.g. originating in Markov processes or Langevin dynamics), frenesy is associated with the time-symmetric part of the action functional, containing trajectory-dependent terms such as escape rates, undirected traffic and the total number of configuration changes. As with many physical observables, it is the change in frenesy that makes the relevant quantity, particularly in the context of non-equilibrium response theory.[1][citation needed]

The role of dynamical activity in trajectory ensembles was explored in the study of large deviations.[4][5] The specific need for dealing with the time-symmetric fluctuation sector was explained in an early influential paper.[6] For some time, it was discussed under the name "traffic", for example, in several studies on macroscopic fluctuations.[7][8] A year later, in the context of response theory, the term "frenetic" appeared.[9]

Mathematically, in a stochastic trajectory under local detailed balance, entropy production is tied to the asymmetry between forward and time-reversed paths, whereas frenesy quantifies the symmetric part invariant under time reversal. As such, it measures changes in dynamical activity or quiescence depending on the reference process and on the level of description.[citation needed]

Role in fluctuation-response

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Frenesy is used in the generalization of fluctuation-dissipation relations beyond equilibrium. In non-equilibrium steady states, the linear response of an observable depends not only on the correlation with entropy production but also on correlations with frenesy. This correction was proposed to describe response phenomena when systems are driven far from equilibrium.[citation needed]

As an extension of Kubo and Green-Kubo formulas, non-equilibrium linear response theory allows the response to be decomposed into an "entropic" term and a "frenetic" term. The frenetic component is absent in equilibrium but becomes significant under external driving forces.[citation needed] This is evident in non-equilibrium modifications of the Sutherland-Einstein relation, where mobility is no longer determined solely by the diffusion matrix of the unperturbed system but also includes force–current correlations.[10] The frenetic contribution can lead to negative responses, such as for differential mobility or non-equilibrium specific heats. This phenomenon, which is often described as "pushing more for getting less"[11] is supported by similar theoretical considerations.[12] Frenetic effects also appear in second order and higher-order nonlinear response expansions around equilibrium.[13][14]

A frenetic contribution also appears in corrections to the fluctuation-dissipation relation of the second kind, known as the Einstein relation. The (linear) friction has an entropic and frenetic part, where the entropic part connects with the noise in the usual equilibrium way. The frenetic part may be negative and dominating to the extent of rendering the friction negative.[15]

Applications

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The concept of frenesy is used in various areas of modern statistical physics. In the presence of dissipation, kinetic aspects in the form of increased or decreased dynamical activity and reactivities can determine a system's behavior.[citation needed] For example, jamming, localization, or glassy behavior are induced by dynamical heterogeneities where traps become important under driving or relaxation. Relaxation behavior is indeed another instance where kinetic aspects matter and where frenesy influences and shapes the landscape of possible pathways.[16] Kinetic phase transitions are governed by large deviations in frenesy that signal transitions between dynamical phases. In active matter, persistent motion is triggered by switches (discrete or continuous) introducing high frenetic activity.[citation needed]

Other applications concern selection and steering.[17] Kinetic proofreading and biological error correction are examples. The presence of driving allows changes in parameters governing dynamical activity to promote certain conditions of occupation and current. When those parameters depend on and receive feedback about the actual state, the system may evolve into a different phase or develop a dynamical pattern, as witnessed in active matter.

The concept of time-symmetric dynamical activity in non-equilibrium statistical mechanics has also been explored in the study of dynamical fluctuation symmetries. It deviates from stochastic thermodynamics by stressing kinetic aspects.[citation needed]

See also

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References

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  1. ^ a b Maes, Christian (2020-03-27). "Frenesy: Time-symmetric dynamical activity in nonequilibria". Physics Reports. Frenesy: time-symmetric dynamical activity in nonequilibria. 850: 1–33. arXiv:1904.10485. doi:10.1016/j.physrep.2020.01.002. ISSN 0370-1573.
  2. ^ Roldán, Édgar; Vivo, Pierpaolo (2019). "Exact Distributions of Currents and Frenesy for Markov Bridges". Physical Review E. 100 (4): 042108. arXiv:1903.08271. Bibcode:2019PhRvE.100d2108R. doi:10.1103/PhysRevE.100.042108. PMID 31770868.
  3. ^ Gaspard, Pierre (2022). The Statistical Mechanics of Irreversible Phenomena. Cambridge University Press. ISBN 9781108563055.
  4. ^ Garrahan, J. P.; Jack, R. L.; Lecomte, V.; Pitard, E.; Van Duijvendijk, K.; Van Wijland, F. (2007). "Dynamical First-Order Phase Transition in Kinetically Constrained Models of Glasses". Physical Review Letters. 98 (19): 195702. arXiv:cond-mat/0701757. Bibcode:2007PhRvL..98s5702G. doi:10.1103/PhysRevLett.98.195702. PMID 17677633.
  5. ^ Garrahan, Juan P.; Jack, Robert L.; Lecomte, Vivien; Pitard, Estelle; Van Duijvendijk, Kristina; Van Wijland, Frédéric (2009). "First-order dynamical phase transition in models of glasses: An approach based on ensembles of histories". Journal of Physics A: Mathematical and Theoretical. 42 (7). arXiv:0810.5298. Bibcode:2009JPhA...42g5007G. doi:10.1088/1751-8113/42/7/075007.
  6. ^ Maes, Christian; Van Wieren, Maarten H. (2006). "Time-Symmetric Fluctuations in Nonequilibrium Systems". Physical Review Letters. 96 (24): 240601. arXiv:cond-mat/0601299. Bibcode:2006PhRvL..96x0601M. doi:10.1103/PhysRevLett.96.240601. PMID 16907225.
  7. ^ Maes, Christian; Netočný, Karel; Wynants, Bram (2008). "Steady state statistics of driven diffusions". Physica A: Statistical Mechanics and Its Applications. 387 (12): 2675–2689. arXiv:0708.0489. Bibcode:2008PhyA..387.2675M. doi:10.1016/j.physa.2008.01.097.
  8. ^ Maes, C.; Netočný, K. (2008). "Canonical structure of dynamical fluctuations in mesoscopic nonequilibrium steady states". Europhysics Letters. 82 (3): 30003. arXiv:0705.2344. Bibcode:2008EL.....8230003M. doi:10.1209/0295-5075/82/30003.
  9. ^ Baiesi, Marco; Maes, Christian; Wynants, Bram (2009). "Fluctuations and Response of Nonequilibrium States". Physical Review Letters. 103 (1): 010602. arXiv:0902.3955. Bibcode:2009PhRvL.103a0602B. doi:10.1103/PhysRevLett.103.010602. PMID 19659132.
  10. ^ Baiesi, Marco; Maes, Christian; Wynants, Bram (2011). "The modified Sutherland–Einstein relation for diffusive non-equilibria". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 467 (2134): 2792–2809. arXiv:1101.3227. Bibcode:2011RSPSA.467.2792B. doi:10.1098/rspa.2011.0046.
  11. ^ Zia, R. K. P.; Praestgaard, E. L.; Mouritsen, O. G. (2002). "Getting more from pushing less: Negative specific heat and conductivity in nonequilibrium steady states". American Journal of Physics. 70 (4): 384–392. arXiv:cond-mat/0108502. Bibcode:2002AmJPh..70..384Z. doi:10.1119/1.1427088.
  12. ^ Baerts, Pieter; Basu, Urna; Maes, Christian; Safaverdi, Soghra (2013). "Frenetic origin of negative differential response". Physical Review E. 88 (5): 052109. arXiv:1308.5613. Bibcode:2013PhRvE..88e2109B. doi:10.1103/PhysRevE.88.052109. PMID 24329216.
  13. ^ Basu, Urna; Krüger, Matthias; Lazarescu, Alexandre; Maes, Christian (2015). "Frenetic aspects of second order response". Physical Chemistry Chemical Physics. 17 (9): 6653–6666. arXiv:1410.7450. Bibcode:2015PCCP...17.6653B. doi:10.1039/C4CP04977B. PMID 25666909.
  14. ^ Müller, Fenna; Basu, Urna; Sollich, Peter; Krüger, Matthias (2020). "Coarse-grained second-order response theory". Physical Review Research. 2 (4): 043123. arXiv:2005.05169. Bibcode:2020PhRvR...2d3123M. doi:10.1103/PhysRevResearch.2.043123.
  15. ^ Pei, Ji-Hui; Maes, Christian (2025). "Induced friction on a probe moving in a nonequilibrium medium". Physical Review E. 111 (3): L032101. arXiv:2407.09989. Bibcode:2025PhRvE.111c2101P. doi:10.1103/PhysRevE.111.L032101. PMID 40247552.
  16. ^ Maes, Christian (2017). "Frenetic Bounds on the Entropy Production". Physical Review Letters. 119 (16) 160601. arXiv:1705.07412. Bibcode:2017PhRvL.119p0601M. doi:10.1103/PhysRevLett.119.160601. PMID 29099195.
  17. ^ Lefebvre, Bram; Maes, Christian (2024). "Frenetic steering: Nonequilibrium-enabled navigation". Chaos: An Interdisciplinary Journal of Nonlinear Science. 34 (6). arXiv:2309.09227. Bibcode:2024Chaos..34f3121L. doi:10.1063/5.0177223. PMID 38848269.

Further reading

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