Statistical-mechanical theory of irreversible processes. I. general theory and simple applications to magnetic and conduction problems
Abstract
A general type of fluctuation-dissipation theorem is discussed to show that the physical quantities such as complex susceptibility of magnetic or electric polarization and complex conductivity for electric conduction are rigorously expressed in terms of time-fluctuation of dynamical variables associated with such irreversible processes. This is a generalization of statistical mechanics which affords exact formulation as the basis of calculation of such irreversible quantities from atomistic theory. The general formalism of this statistical-mechanical theory is examined in detail. The response, relaxation, and correlation functions are defined in quantummechanical way and their relations are investigated. The formalism is illustrated by simple examples of magnetic and conduction problems. Certain sum rules are discussed for these examples. Finally it is pointed out that this theory may be looked as a generalization of the Einstein relation.
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Any physical system shows some degree of memory in its response to external perturbations, whether that memory is easy to detect or not.
“any physical system shows some degree of memory in its response to external perturbations [12], whether that memory is easy to detect or not.”
From Comment on 'If it's pinched it's a memristor' (2019) · cites this paper as [12]
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Comment on 'If it's pinched it's a memristor'
Pershin, Y. V., & Ventra, M. D. (2019) · Semiconductor Science and Technology · doi:10.1088/1361-6641/ab3584 · Cited by 10 · see citing works
“mory response [6]. This is not an assumption or a mathematical denition. It is a matter of physical reality: any physical system shows some degree of memory in its response to external perturbations [12], whether that memory is easy to detect or not. Therefore, since theoretical models have to correspond to an actual…”
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- Authors
- Kubo, R.
- Affiliations
- The University of Tokyo (JP)
- Corresponding author
- Kubo, Ryogo
- ORCID
- Kubo, Ryogo
- Venue
- Journal of the Physical Society of Japan
- Publisher
- Physical Society of Japan
- Published
- 1957-06
- Volume
- 12
- Issue
- 6
- Pages
- 570-586
- ISSN
- 0031-9015 (ISSN-L)
- 1347-4073
- OpenAlex
- W2018763953
- Cited by
- 9,441
- References
- 0
- Citations by year
- 2026: 343 · 2025: 418 · 2024: 350 · 2023: 363 · 2022: 385 · 2021: 398 · 2020: 470 · 2019: 310 · 2018: 262 · 2017: 310 · 2016: 273 · 2015: 239 · 2014: 237 · 2013: 212 · 2012: 239
- FWCI
- 24.58
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the Physical Society of Japan (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
- Keywords
- fluctuation-dissipation theorem, irreversible processes, complex susceptibility, complex conductivity, magnetic polarization, electrical conduction, response functions, relaxation function, correlation functions, sum rules, Einstein relation, generalized statistical mechanics
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