the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 15 Nov 2022
Review article: large fluctuations in non-equilibrium physics
Abstract. Non-equilibrium is dominant in geophysical and climate phenomena. However the study of non-equilibrium is much more difficult than equilibrium and the relevance of probabilistic simplified models has been emphasized. Large deviation rates have been used recently in climate science. In this paper after recalling progress during the last decades in understanding the role of large deviations in a class of non-equilibrium systems we point out differences between equilibrium and non-equilibrium. For example in non-equilibrium: a) large deviation rates may be extensive but not simply additive. b) In non-equilibrium there are generically long range space correlations so large deviation rates are non-local. c) Singularities in large deviation rates denote the existence of phase transitions often not possible in equilibrium. To exemplify we shall refer to lattice gas models like the symmetric simple exclusion process and other models which are playing an important role in the understanding of non-equilibrium physics. Reasons why all this may be of interest in climate physics will be briefly indicated.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
(460 KB)
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(460 KB) - Metadata XML
- BibTeX
- EndNote
- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2022-1192', Anonymous Referee #1, 15 Nov 2022
This is a very clear and nice review of works done over the last 20 years. I think it should be published as it is.
I found only very few misprints :
line 69 applicaton -> application
line 200 J(rho(t) -> J(rho(t))
line 232 e phenomenon -> a phenomenon
line 293-294 there is an unnecessary break
Citation: https://doi.org/10.5194/egusphere-2022-1192-RC1 -
RC2: 'Comment on egusphere-2022-1192', Valerio Lucarini, 07 Feb 2023
The paper by G. Jona-Lasinio present a succinct and most useful summary of recent development in large deviation theory for nonequilibrium systems. It is well-written and very clear. This contribution can and will provide inspiration for scientists across the whole spectrum of geosciences. I am including in the .pdf file some friendly comments that are aimed at either encouraging the author to clarify some part of the text for the reader who is less familiar with the topic, or suggesting some geophysical context to the concepts and ideas presented in the article.
Valerio Lucarini
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AC1: 'Comment on egusphere-2022-1192', Gianni Jona-Lasinio, 15 Mar 2023
As far as the first anonymous referee is concerned I have nothing to say as he recommends publication of my paper
To the second referee, Valerio Lucarini, my answers to his remarks are
Line 26 - reaction-diffusion systems - please tell me which you consider the relevant references to add to the bibliography
Line 52 - local equilibrium - I will add the reference to Ghil and Lucarini 2020
where local equilibrium is not mentioned explicitely but is implied in several discussionsLine 102 - $F_{0}$ is the equilibrium free energy which is different for different systems
Line 119 - non--equilibrium is due to both the external field and the boundary conditions
Line 124 - the chemical potential in most of the models considered describes the interaction with the external reservoirs according to eq. (7)
Line 146 - the quantity $\epsilon^{-d}$ is extensive in space. A factor extensive in time appears in fluctuations of time averaged quantities.
Line 169 - this formulation represents at the mesoscopic level a form of detailed balance in non--equilibrium
Line 180 - I will add the definition of the Lagrangian
Line 188 - I will add a reference
Line 202 - this is the energy dissipated by the fluctuation, not the total dissipated energy
Line 224 - to which intermediate points and constraints are you referring?
Line 235 - Summable with respect to space variables. I will add a comment on the analogy with critical phenomena
Line 241 - I will add a reference
Line 261 - The effect of long range correlations is that local thermodynamic variables are not independent at macroscopic distances
Line 294 - no, Q is the amount of particles through the origin which in an interval of time t for a diffusion process is of the order of square root of t.
Line 345 - ok. Which references would you like to be mentioned, those of Line 26 ?
Citation: https://doi.org/10.5194/egusphere-2022-1192-AC1
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2022-1192', Anonymous Referee #1, 15 Nov 2022
This is a very clear and nice review of works done over the last 20 years. I think it should be published as it is.
I found only very few misprints :
line 69 applicaton -> application
line 200 J(rho(t) -> J(rho(t))
line 232 e phenomenon -> a phenomenon
line 293-294 there is an unnecessary break
Citation: https://doi.org/10.5194/egusphere-2022-1192-RC1 -
RC2: 'Comment on egusphere-2022-1192', Valerio Lucarini, 07 Feb 2023
The paper by G. Jona-Lasinio present a succinct and most useful summary of recent development in large deviation theory for nonequilibrium systems. It is well-written and very clear. This contribution can and will provide inspiration for scientists across the whole spectrum of geosciences. I am including in the .pdf file some friendly comments that are aimed at either encouraging the author to clarify some part of the text for the reader who is less familiar with the topic, or suggesting some geophysical context to the concepts and ideas presented in the article.
Valerio Lucarini
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AC1: 'Comment on egusphere-2022-1192', Gianni Jona-Lasinio, 15 Mar 2023
As far as the first anonymous referee is concerned I have nothing to say as he recommends publication of my paper
To the second referee, Valerio Lucarini, my answers to his remarks are
Line 26 - reaction-diffusion systems - please tell me which you consider the relevant references to add to the bibliography
Line 52 - local equilibrium - I will add the reference to Ghil and Lucarini 2020
where local equilibrium is not mentioned explicitely but is implied in several discussionsLine 102 - $F_{0}$ is the equilibrium free energy which is different for different systems
Line 119 - non--equilibrium is due to both the external field and the boundary conditions
Line 124 - the chemical potential in most of the models considered describes the interaction with the external reservoirs according to eq. (7)
Line 146 - the quantity $\epsilon^{-d}$ is extensive in space. A factor extensive in time appears in fluctuations of time averaged quantities.
Line 169 - this formulation represents at the mesoscopic level a form of detailed balance in non--equilibrium
Line 180 - I will add the definition of the Lagrangian
Line 188 - I will add a reference
Line 202 - this is the energy dissipated by the fluctuation, not the total dissipated energy
Line 224 - to which intermediate points and constraints are you referring?
Line 235 - Summable with respect to space variables. I will add a comment on the analogy with critical phenomena
Line 241 - I will add a reference
Line 261 - The effect of long range correlations is that local thermodynamic variables are not independent at macroscopic distances
Line 294 - no, Q is the amount of particles through the origin which in an interval of time t for a diffusion process is of the order of square root of t.
Line 345 - ok. Which references would you like to be mentioned, those of Line 26 ?
Citation: https://doi.org/10.5194/egusphere-2022-1192-AC1
Peer review completion
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Giovanni Jona-Lasinio
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(460 KB) - Metadata XML