---
_id: '12216'
abstract:
- lang: eng
  text: Many trace inequalities can be expressed either as concavity/convexity theorems
    or as monotonicity theorems. A classic example is the joint convexity of the quantum
    relative entropy which is equivalent to the Data Processing Inequality. The latter
    says that quantum operations can never increase the relative entropy. The monotonicity
    versions often have many advantages, and often have direct physical application,
    as in the example just mentioned. Moreover, the monotonicity results are often
    valid for a larger class of maps than, say, quantum operations (which are completely
    positive). In this paper we prove several new monotonicity results, the first
    of which is a monotonicity theorem that has as a simple corollary a celebrated
    concavity theorem of Epstein. Our starting points are the monotonicity versions
    of the Lieb Concavity and the Lieb Convexity Theorems. We also give two new proofs
    of these in their general forms using interpolation. We then prove our new monotonicity
    theorems by several duality arguments.
acknowledgement: Work partially supported by the Lise Meitner fellowship, Austrian
  Science Fund (FWF) M3337.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Eric A.
  full_name: Carlen, Eric A.
  last_name: Carlen
- first_name: Haonan
  full_name: Zhang, Haonan
  id: D8F41E38-9E66-11E9-A9E2-65C2E5697425
  last_name: Zhang
citation:
  ama: Carlen EA, Zhang H. Monotonicity versions of Epstein’s concavity theorem and
    related inequalities. <i>Linear Algebra and its Applications</i>. 2022;654:289-310.
    doi:<a href="https://doi.org/10.1016/j.laa.2022.09.001">10.1016/j.laa.2022.09.001</a>
  apa: Carlen, E. A., &#38; Zhang, H. (2022). Monotonicity versions of Epstein’s concavity
    theorem and related inequalities. <i>Linear Algebra and Its Applications</i>.
    Elsevier. <a href="https://doi.org/10.1016/j.laa.2022.09.001">https://doi.org/10.1016/j.laa.2022.09.001</a>
  chicago: Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s
    Concavity Theorem and Related Inequalities.” <i>Linear Algebra and Its Applications</i>.
    Elsevier, 2022. <a href="https://doi.org/10.1016/j.laa.2022.09.001">https://doi.org/10.1016/j.laa.2022.09.001</a>.
  ieee: E. A. Carlen and H. Zhang, “Monotonicity versions of Epstein’s concavity theorem
    and related inequalities,” <i>Linear Algebra and its Applications</i>, vol. 654.
    Elsevier, pp. 289–310, 2022.
  ista: Carlen EA, Zhang H. 2022. Monotonicity versions of Epstein’s concavity theorem
    and related inequalities. Linear Algebra and its Applications. 654, 289–310.
  mla: Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s Concavity
    Theorem and Related Inequalities.” <i>Linear Algebra and Its Applications</i>,
    vol. 654, Elsevier, 2022, pp. 289–310, doi:<a href="https://doi.org/10.1016/j.laa.2022.09.001">10.1016/j.laa.2022.09.001</a>.
  short: E.A. Carlen, H. Zhang, Linear Algebra and Its Applications 654 (2022) 289–310.
date_created: 2023-01-16T09:46:38Z
date_published: 2022-12-01T00:00:00Z
date_updated: 2023-08-04T09:24:51Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1016/j.laa.2022.09.001
external_id:
  isi:
  - '000860689600014'
file:
- access_level: open_access
  checksum: cf3cb7e7e34baa967849f01d8f0c1ae4
  content_type: application/pdf
  creator: dernst
  date_created: 2023-01-27T08:08:39Z
  date_updated: 2023-01-27T08:08:39Z
  file_id: '12415'
  file_name: 2022_LinearAlgebra_Carlen.pdf
  file_size: 441184
  relation: main_file
  success: 1
file_date_updated: 2023-01-27T08:08:39Z
has_accepted_license: '1'
intvolume: '       654'
isi: 1
keyword:
- Discrete Mathematics and Combinatorics
- Geometry and Topology
- Numerical Analysis
- Algebra and Number Theory
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 289-310
project:
- _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6
  grant_number: M03337
  name: Curvature-dimension in noncommutative analysis
publication: Linear Algebra and its Applications
publication_identifier:
  issn:
  - 0024-3795
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Monotonicity versions of Epstein's concavity theorem and related inequalities
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 654
year: '2022'
...
---
_id: '11556'
abstract:
- lang: eng
  text: "We revisit two basic Direct Simulation Monte Carlo Methods to model aggregation
    kinetics and extend them for aggregation processes with collisional fragmentation
    (shattering). We test the performance and accuracy of the extended methods and
    compare their performance with efficient deterministic finite-difference method
    applied to the same model. We validate the stochastic methods on the test problems
    and apply them to verify the existence of oscillating regimes in the aggregation-fragmentation
    kinetics recently detected in deterministic simulations. We confirm the emergence
    of steady oscillations of densities in such systems and prove the stability of
    the\r\noscillations with respect to fluctuations and noise."
acknowledgement: Zhores supercomputer of Skolkovo Institute of Science and Technology
  [68] has been used in the present research. S.A.M. was supported by Moscow Center
  for Fundamental and Applied Mathematics (the agreement with the Ministry of Education
  and Science of the Russian Federation No. 075-15-2019-1624). A.I.O. acknowledges
  RFBR project No. 20-31-90022. N.V.B. acknowledges the support of the Analytical
  Center (subsidy agreement 000000D730321P5Q0002, Grant No. 70-2021-00145 02.11.2021).
article_number: '111439'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Aleksei
  full_name: Kalinov, Aleksei
  id: 44b7120e-eb97-11eb-a6c2-e1557aa81d02
  last_name: Kalinov
  orcid: 0000-0003-2189-3904
- first_name: A.I.
  full_name: Osinskiy, A.I.
  last_name: Osinskiy
- first_name: S.A.
  full_name: Matveev, S.A.
  last_name: Matveev
- first_name: W.
  full_name: Otieno, W.
  last_name: Otieno
- first_name: N.V.
  full_name: Brilliantov, N.V.
  last_name: Brilliantov
citation:
  ama: Kalinov A, Osinskiy AI, Matveev SA, Otieno W, Brilliantov NV. Direct simulation
    Monte Carlo for new regimes in aggregation-fragmentation kinetics. <i>Journal
    of Computational Physics</i>. 2022;467. doi:<a href="https://doi.org/10.1016/j.jcp.2022.111439">10.1016/j.jcp.2022.111439</a>
  apa: Kalinov, A., Osinskiy, A. I., Matveev, S. A., Otieno, W., &#38; Brilliantov,
    N. V. (2022). Direct simulation Monte Carlo for new regimes in aggregation-fragmentation
    kinetics. <i>Journal of Computational Physics</i>. Elsevier. <a href="https://doi.org/10.1016/j.jcp.2022.111439">https://doi.org/10.1016/j.jcp.2022.111439</a>
  chicago: Kalinov, Aleksei, A.I. Osinskiy, S.A. Matveev, W. Otieno, and N.V. Brilliantov.
    “Direct Simulation Monte Carlo for New Regimes in Aggregation-Fragmentation Kinetics.”
    <i>Journal of Computational Physics</i>. Elsevier, 2022. <a href="https://doi.org/10.1016/j.jcp.2022.111439">https://doi.org/10.1016/j.jcp.2022.111439</a>.
  ieee: A. Kalinov, A. I. Osinskiy, S. A. Matveev, W. Otieno, and N. V. Brilliantov,
    “Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics,”
    <i>Journal of Computational Physics</i>, vol. 467. Elsevier, 2022.
  ista: Kalinov A, Osinskiy AI, Matveev SA, Otieno W, Brilliantov NV. 2022. Direct
    simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics.
    Journal of Computational Physics. 467, 111439.
  mla: Kalinov, Aleksei, et al. “Direct Simulation Monte Carlo for New Regimes in
    Aggregation-Fragmentation Kinetics.” <i>Journal of Computational Physics</i>,
    vol. 467, 111439, Elsevier, 2022, doi:<a href="https://doi.org/10.1016/j.jcp.2022.111439">10.1016/j.jcp.2022.111439</a>.
  short: A. Kalinov, A.I. Osinskiy, S.A. Matveev, W. Otieno, N.V. Brilliantov, Journal
    of Computational Physics 467 (2022).
date_created: 2022-07-11T12:19:59Z
date_published: 2022-10-15T00:00:00Z
date_updated: 2023-08-03T11:55:06Z
day: '15'
ddc:
- '518'
department:
- _id: GradSch
- _id: ChWo
doi: 10.1016/j.jcp.2022.111439
external_id:
  arxiv:
  - '2103.09481'
  isi:
  - '000917225500013'
intvolume: '       467'
isi: 1
keyword:
- Computer Science Applications
- Physics and Astronomy (miscellaneous)
- Applied Mathematics
- Computational Mathematics
- Modeling and Simulation
- Numerical Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2103.09481
month: '10'
oa: 1
oa_version: Preprint
publication: Journal of Computational Physics
publication_identifier:
  issn:
  - 0021-9991
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: Direct simulation Monte Carlo for new regimes in aggregation-fragmentation
  kinetics
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 467
year: '2022'
...