---
OA_place: publisher
_id: '20563'
abstract:
- lang: eng
text: "The theory of optimal transport provides an elegant and powerful description
of many evolution\r\nequations as gradient flows. The primary objective of this
thesis is to adapt and extend the\r\ntheory to deal with important equations that
are not covered by the classical framework,\r\nspecifically boundary value problems
and kinetic equations. Additionally, we establish new\r\nresults in periodic homogenization
for discrete dynamical optimal transport and in quantization\r\nof measures.\r\nSection
1.1 serves as an invitation to the classical theory of optimal transport, including
the\r\nmain definitions and a selection of well-established theorems. Sections
1.2-1.5 introduce the\r\nmain results of this thesis, outline the motivations,
and review the current state of the art.\r\nIn Chapter 2, we consider the Fokker–Planck
equation on a bounded set with positive Dirichlet\r\nboundary conditions. We construct
a time-discrete scheme involving a modification of the\r\nWasserstein distance
and, under weak assumptions, prove its convergence to a solution of this\r\nboundary
value problem. In dimension 1, we show that this solution is a gradient flow in
a\r\nsuitable space of measures.\r\nChapter 3 presents joint work with Giovanni
Brigati and Jan Maas. We introduce a new theory\r\nof optimal transport to describe
and study particle systems at the mesoscopic scale. We prove\r\nadapted versions
of some fundamental theorems, including the Benamou–Brenier formula and\r\nthe
identification of absolutely continuous curves of measures.\r\nChapter 4 presents
joint work with Lorenzo Portinale. We prove convergence of dynamical\r\ntransportation
functionals on periodic graphs in the large-scale limit when the cost functional\r\nis
asymptotically linear. Additionally, we show that discrete 1-Wasserstein distances
converge\r\nto 1-Wasserstein distances constructed from crystalline norms on R\r\nd\r\n.\r\nChapter
5 concerns optimal empirical quantization: the problem of approximating a measure\r\nby
the sum of n equally weighted Dirac deltas, so as to minimize the error in the
p-Wasserstein\r\ndistance. Our main result is an analog of Zador’s theorem, providing
asymptotic bounds for\r\nthe minimal error as n tends to infinity.\r\n"
acknowledgement: "The research contained in this thesis has received funding from
the Austrian Science\r\nFund (FWF) project 10.55776/F65."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Filippo
full_name: Quattrocchi, Filippo
id: 3ebd6ba8-edfb-11eb-afb5-91a9745ba308
last_name: Quattrocchi
orcid: 0009-0000-9773-1931
citation:
ama: Quattrocchi F. Optimal transport methods for kinetic equations, boundary value
problems, and discretization of measures. 2025. doi:10.15479/AT-ISTA-20563
apa: Quattrocchi, F. (2025). Optimal transport methods for kinetic equations,
boundary value problems, and discretization of measures. Institute of Science
and Technology Austria. https://doi.org/10.15479/AT-ISTA-20563
chicago: Quattrocchi, Filippo. “Optimal Transport Methods for Kinetic Equations,
Boundary Value Problems, and Discretization of Measures.” Institute of Science
and Technology Austria, 2025. https://doi.org/10.15479/AT-ISTA-20563.
ieee: F. Quattrocchi, “Optimal transport methods for kinetic equations, boundary
value problems, and discretization of measures,” Institute of Science and Technology
Austria, 2025.
ista: Quattrocchi F. 2025. Optimal transport methods for kinetic equations, boundary
value problems, and discretization of measures. Institute of Science and Technology
Austria.
mla: Quattrocchi, Filippo. Optimal Transport Methods for Kinetic Equations, Boundary
Value Problems, and Discretization of Measures. Institute of Science and Technology
Austria, 2025, doi:10.15479/AT-ISTA-20563.
short: F. Quattrocchi, Optimal Transport Methods for Kinetic Equations, Boundary
Value Problems, and Discretization of Measures, Institute of Science and Technology
Austria, 2025.
corr_author: '1'
date_created: 2025-10-28T13:10:49Z
date_published: 2025-11-03T00:00:00Z
date_updated: 2026-04-07T12:39:35Z
day: '03'
ddc:
- '515'
- '519'
degree_awarded: PhD
department:
- _id: GradSch
- _id: JaMa
doi: 10.15479/AT-ISTA-20563
file:
- access_level: open_access
checksum: 6f55275bdf99992be3a6457d949dd664
content_type: application/pdf
creator: fquattro
date_created: 2025-11-17T21:04:15Z
date_updated: 2026-01-01T23:30:03Z
embargo: 2026-01-01
file_id: '20653'
file_name: 2025_quattrocchi_filippo_thesis.pdf
file_size: 4326411
relation: main_file
- access_level: closed
checksum: 707e580f5d993a214c0dba456b75837b
content_type: application/zip
creator: fquattro
date_created: 2025-11-17T21:05:43Z
date_updated: 2026-01-01T23:30:03Z
embargo_to: open_access
file_id: '20654'
file_name: 2025_quattrocchi_thesis.zip
file_size: 11726509
relation: source_file
file_date_updated: 2026-01-01T23:30:03Z
has_accepted_license: '1'
keyword:
- optimal transport
- kinetic equations
- boundary value problems
- quantization
- gradient flows
- homogenization
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: '240'
project:
- _id: 260482E2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: F06504
name: Taming Complexity in Partial Differential Systems
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '18706'
relation: part_of_dissertation
status: public
- id: '20569'
relation: part_of_dissertation
status: public
- id: '20571'
relation: part_of_dissertation
status: public
- id: '20570'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
title: Optimal transport methods for kinetic equations, boundary value problems, and
discretization of measures
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: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '20571'
abstract:
- lang: eng
text: "We prove the convergence of a modified Jordan--Kinderlehrer--Otto scheme
to a solution to the Fokker--Planck equation in $\\Omega \\Subset \\mathbb{R}^d$
with general, positive and temporally constant, Dirichlet boundary conditions.
We work under mild assumptions on the domain, the drift, and the initial datum.
\ In the special case where $\\Omega$ is an interval in $\\mathbb{R}^1$, we prove
that such a solution is a gradient flow -- curve of maximal slope -- within a
suitable space of measures, endowed with a modified Wasserstein distance.\r\nOur
discrete scheme and modified distance draw inspiration from contributions by A.
Figalli and N. Gigli [J. Math. Pures Appl. 94, (2010), pp. 107--130], and J. Morales
[J. Math. Pures Appl. 112, (2018), pp. 41--88] on an optimal-transport approach
to evolution equations with Dirichlet boundary conditions. Similarly to these
works, we allow the mass to flow from/to the boundary $\\partial \\Omega$ throughout
the evolution. However, our leading idea is to also keep track of the mass at
the boundary by working with measures defined on the whole closure $\\overline
\\Omega$. The driving functional is a modification of the classical relative entropy
that also makes use of the information at the boundary. As an intermediate result,
when $\\Omega$ is an interval in $\\mathbb{R}^1$, we find a formula for the descending
slope of this geodesically nonconvex functional. "
acknowledgement: "The author would like to thank Jan Maas for suggesting this project
and for many helpful\r\ncomments, Antonio Agresti, Lorenzo Dello Schiavo and Julian
Fischer for several fruitful discussions, and Oliver Tse for pointing out the reference
[15]. He also gratefully acknowledges support from the Austrian Science Fund (FWF)
project 10.55776/F65.\r\n"
article_number: '2403.07803'
article_processing_charge: No
arxiv: 1
author:
- first_name: Filippo
full_name: Quattrocchi, Filippo
id: 3ebd6ba8-edfb-11eb-afb5-91a9745ba308
last_name: Quattrocchi
orcid: 0009-0000-9773-1931
citation:
ama: Quattrocchi F. Variational structures for the Fokker-Planck equation with general
Dirichlet boundary conditions. arXiv. doi:10.48550/arXiv.2403.07803
apa: Quattrocchi, F. (n.d.). Variational structures for the Fokker-Planck equation
with general Dirichlet boundary conditions. arXiv. https://doi.org/10.48550/arXiv.2403.07803
chicago: Quattrocchi, Filippo. “Variational Structures for the Fokker-Planck Equation
with General Dirichlet Boundary Conditions.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2403.07803.
ieee: F. Quattrocchi, “Variational structures for the Fokker-Planck equation with
general Dirichlet boundary conditions,” arXiv. .
ista: Quattrocchi F. Variational structures for the Fokker-Planck equation with
general Dirichlet boundary conditions. arXiv, 2403.07803.
mla: Quattrocchi, Filippo. “Variational Structures for the Fokker-Planck Equation
with General Dirichlet Boundary Conditions.” ArXiv, 2403.07803, doi:10.48550/arXiv.2403.07803.
short: F. Quattrocchi, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-10-28T13:12:56Z
date_published: 2024-04-09T00:00:00Z
date_updated: 2026-04-27T22:30:15Z
day: '09'
department:
- _id: GradSch
- _id: JaMa
doi: 10.48550/arXiv.2403.07803
external_id:
arxiv:
- '2403.07803'
keyword:
- gradient flows
- Jordan–Kinderlehrer–Otto scheme
- curves of maximal slope
- optimal transport
- Dirichlet boundary conditions
- Fokker–Planck equation
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2403.07803
month: '04'
oa: 1
oa_version: Preprint
project:
- _id: 260482E2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: F06504
name: Taming Complexity in Partial Differential Systems
publication: arXiv
publication_status: draft
related_material:
record:
- id: '20865'
relation: later_version
status: public
- id: '20563'
relation: dissertation_contains
status: public
status: public
title: Variational structures for the Fokker-Planck equation with general Dirichlet
boundary conditions
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '20570'
abstract:
- lang: eng
text: "We investigate the minimal error in approximating a general probability\r\nmeasure
$\\mu$ on $\\mathbb{R}^d$ by the uniform measure on a finite set with\r\nprescribed
cardinality $n$. The error is measured in the $p$-Wasserstein\r\ndistance. In
particular, when $1\\le parXiv. doi:10.48550/arXiv.2408.12924
apa: Quattrocchi, F. (n.d.). Asymptotics for optimal empirical quantization of measures.
arXiv. https://doi.org/10.48550/arXiv.2408.12924
chicago: Quattrocchi, Filippo. “Asymptotics for Optimal Empirical Quantization of
Measures.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2408.12924.
ieee: F. Quattrocchi, “Asymptotics for optimal empirical quantization of measures,”
arXiv. .
ista: Quattrocchi F. Asymptotics for optimal empirical quantization of measures.
arXiv, 2408.12924.
mla: Quattrocchi, Filippo. “Asymptotics for Optimal Empirical Quantization of Measures.”
ArXiv, 2408.12924, doi:10.48550/arXiv.2408.12924.
short: F. Quattrocchi, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-10-28T13:12:22Z
date_published: 2024-08-23T00:00:00Z
date_updated: 2026-04-27T22:30:15Z
day: '23'
department:
- _id: GradSch
- _id: JaMa
doi: 10.48550/arXiv.2408.12924
external_id:
arxiv:
- '2408.12924'
keyword:
- optimal empirical quantization
- vector quantization
- Wasserstein distance
- semidiscrete optimal transport
- Zador’s Theorem
- Pierce’s Lemma
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2408.12924
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: 260482E2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: F06504
name: Taming Complexity in Partial Differential Systems
publication: arXiv
publication_status: draft
related_material:
record:
- id: '20563'
relation: dissertation_contains
status: public
status: public
title: Asymptotics for optimal empirical quantization of measures
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2024'
...
---
_id: '12911'
abstract:
- lang: eng
text: 'This paper establishes new connections between many-body quantum systems,
One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport
(OT), by interpreting the problem of computing the ground-state energy of a finite-dimensional
composite quantum system at positive temperature as a non-commutative entropy
regularized Optimal Transport problem. We develop a new approach to fully characterize
the dual-primal solutions in such non-commutative setting. The mathematical formalism
is particularly relevant in quantum chemistry: numerical realizations of the many-electron
ground-state energy can be computed via a non-commutative version of Sinkhorn
algorithm. Our approach allows to prove convergence and robustness of this algorithm,
which, to our best knowledge, were unknown even in the two marginal case. Our
methods are based on a priori estimates in the dual problem, which we believe
to be of independent interest. Finally, the above results are extended in 1RDMFT
setting, where bosonic or fermionic symmetry conditions are enforced on the problem.'
acknowledgement: "This work started when A.G. was visiting the Erwin Schrödinger Institute
and then continued when D.F. and L.P visited the Theoretical Chemistry Department
of the Vrije Universiteit Amsterdam. The authors thank the hospitality of both places
and, especially, P. Gori-Giorgi and K. Giesbertz for fruitful discussions and literature
suggestions in the early state of the project. The authors also thank J. Maas and
R. Seiringer for their feedback and useful comments to a first draft of the article.
Finally, we acknowledge the high quality review done by the anonymous referee of
our paper, who we would like to thank for the excellent work and constructive feedback.\r\nD.F
acknowledges support by the European Research Council (ERC) under the European Union's
Horizon 2020 research and innovation programme (grant agreements No 716117 and No
694227). A.G. acknowledges funding by the HORIZON EUROPE European Research Council
under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942] as well as partial support of
his research by the Canada Research Chairs Program (ID 2021-00234) and Natural Sciences
and Engineering Research Council of Canada, RGPIN-2022-05207. L.P. acknowledges
support by the Austrian Science Fund (FWF), grants No W1245 and No F65, and by the
Deutsche Forschungsgemeinschaft (DFG) - Project number 390685813."
article_number: '109963'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Dario
full_name: Feliciangeli, Dario
id: 41A639AA-F248-11E8-B48F-1D18A9856A87
last_name: Feliciangeli
orcid: 0000-0003-0754-8530
- first_name: Augusto
full_name: Gerolin, Augusto
last_name: Gerolin
- first_name: Lorenzo
full_name: Portinale, Lorenzo
id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
last_name: Portinale
citation:
ama: Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal
transport approach to quantum composite systems at positive temperature. Journal
of Functional Analysis. 2023;285(4). doi:10.1016/j.jfa.2023.109963
apa: Feliciangeli, D., Gerolin, A., & Portinale, L. (2023). A non-commutative
entropic optimal transport approach to quantum composite systems at positive temperature.
Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2023.109963
chicago: Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative
Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.”
Journal of Functional Analysis. Elsevier, 2023. https://doi.org/10.1016/j.jfa.2023.109963.
ieee: D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic
optimal transport approach to quantum composite systems at positive temperature,”
Journal of Functional Analysis, vol. 285, no. 4. Elsevier, 2023.
ista: Feliciangeli D, Gerolin A, Portinale L. 2023. A non-commutative entropic optimal
transport approach to quantum composite systems at positive temperature. Journal
of Functional Analysis. 285(4), 109963.
mla: Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach
to Quantum Composite Systems at Positive Temperature.” Journal of Functional
Analysis, vol. 285, no. 4, 109963, Elsevier, 2023, doi:10.1016/j.jfa.2023.109963.
short: D. Feliciangeli, A. Gerolin, L. Portinale, Journal of Functional Analysis
285 (2023).
date_created: 2023-05-07T22:01:02Z
date_published: 2023-08-15T00:00:00Z
date_updated: 2025-04-15T08:31:52Z
day: '15'
department:
- _id: RoSe
- _id: JaMa
doi: 10.1016/j.jfa.2023.109963
ec_funded: 1
external_id:
arxiv:
- '2106.11217'
isi:
- '000990804300001'
intvolume: ' 285'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2106.11217
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '694227'
name: Analysis of quantum many-body systems
- _id: 260482E2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: F06504
name: Taming Complexity in Partial Differential Systems
publication: Journal of Functional Analysis
publication_identifier:
eissn:
- 1096-0783
issn:
- 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
record:
- id: '9792'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: A non-commutative entropic optimal transport approach to quantum composite
systems at positive temperature
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 285
year: '2023'
...
---
OA_place: repository
OA_type: green
_id: '20572'
abstract:
- lang: eng
text: "We present an elementary non-recursive formula for the multivariate moments\r\nof
the Dirichlet distribution on the standard simplex, in terms of the pattern\r\ninventory
of the moments' exponents. We obtain analog formulas for the\r\nmultivariate moments
of the Dirichlet-Ferguson and Gamma measures. We further\r\nintroduce a polychromatic
analogue of Ewens sampling formula on colored integer\r\npartitions, discuss its
relation with suitable extensions of Hoppe's urn model\r\nand of the Chinese restaurant
process, and prove that it satisfies an adapted\r\nnotion of consistency in the
sense of Kingman."
acknowledgement: This research was funded by the Austrian Science Fund (FWF) ESPRIT
208. For the purpose of open access, the authors have applied a CC BY public copyright
licence to any Author Accepted Manuscript version arising from this submission.
F.Q. gratefully acknowledges support by the Austrian Science Fund (FWF), Project
SFB F65. The authors are grateful to Professor Nathanaël Berestycki for several
helpful suggestions, and to Nicola Battisti and Dr. Elizabeth Hollwey for enlightening
discussions on DNA-methylation.
article_number: '2309.11292'
article_processing_charge: No
arxiv: 1
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Filippo
full_name: Quattrocchi, Filippo
id: 3ebd6ba8-edfb-11eb-afb5-91a9745ba308
last_name: Quattrocchi
orcid: 0009-0000-9773-1931
citation:
ama: Dello Schiavo L, Quattrocchi F. Multivariate Dirichlet moments and a polychromatic
Ewens sampling formula. arXiv. doi:10.48550/arXiv.2309.11292
apa: Dello Schiavo, L., & Quattrocchi, F. (n.d.). Multivariate Dirichlet moments
and a polychromatic Ewens sampling formula. arXiv. https://doi.org/10.48550/arXiv.2309.11292
chicago: Dello Schiavo, Lorenzo, and Filippo Quattrocchi. “Multivariate Dirichlet
Moments and a Polychromatic Ewens Sampling Formula.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2309.11292.
ieee: L. Dello Schiavo and F. Quattrocchi, “Multivariate Dirichlet moments and a
polychromatic Ewens sampling formula,” arXiv. .
ista: Dello Schiavo L, Quattrocchi F. Multivariate Dirichlet moments and a polychromatic
Ewens sampling formula. arXiv, 2309.11292.
mla: Dello Schiavo, Lorenzo, and Filippo Quattrocchi. “Multivariate Dirichlet Moments
and a Polychromatic Ewens Sampling Formula.” ArXiv, 2309.11292, doi:10.48550/arXiv.2309.11292.
short: L. Dello Schiavo, F. Quattrocchi, ArXiv (n.d.).
corr_author: '1'
date_created: 2025-10-28T13:13:08Z
date_published: 2023-09-20T00:00:00Z
date_updated: 2025-11-24T13:53:48Z
day: '20'
department:
- _id: GradSch
- _id: JaMa
doi: 10.48550/arXiv.2309.11292
external_id:
arxiv:
- '2309.11292'
keyword:
- Dirichlet distribution
- Ewens sampling formula
- Hoppe urn model
- colored partitions
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2309.11292
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
grant_number: E208
name: Configuration Spaces over Non-Smooth Spaces
- _id: 260482E2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: F06504
name: Taming Complexity in Partial Differential Systems
publication: arXiv
publication_status: draft
status: public
title: Multivariate Dirichlet moments and a polychromatic Ewens sampling formula
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '8758'
abstract:
- lang: eng
text: We consider various modeling levels for spatially homogeneous chemical reaction
systems, namely the chemical master equation, the chemical Langevin dynamics,
and the reaction-rate equation. Throughout we restrict our study to the case where
the microscopic system satisfies the detailed-balance condition. The latter allows
us to enrich the systems with a gradient structure, i.e. the evolution is given
by a gradient-flow equation. We present the arising links between the associated
gradient structures that are driven by the relative entropy of the detailed-balance
steady state. The limit of large volumes is studied in the sense of evolutionary
Γ-convergence of gradient flows. Moreover, we use the gradient structures to derive
hybrid models for coupling different modeling levels.
acknowledgement: The research of A.M. was partially supported by the Deutsche Forschungsgemeinschaft
(DFG) via the Collaborative Research Center SFB 1114 Scaling Cascades in Complex
Systems (Project No. 235221301), through the Subproject C05 Effective models for
materials and interfaces with multiple scales. J.M. gratefully acknowledges support
by the European Research Council (ERC) under the European Union’s Horizon 2020 research
and innovation programme (Grant Agreement No. 716117), and by the Austrian Science
Fund (FWF), Project SFB F65. The authors thank Christof Schütte, Robert I. A. Patterson,
and Stefanie Winkelmann for helpful and stimulating discussions. Open access funding
provided by Austrian Science Fund (FWF).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Alexander
full_name: Mielke, Alexander
last_name: Mielke
citation:
ama: Maas J, Mielke A. Modeling of chemical reaction systems with detailed balance
using gradient structures. Journal of Statistical Physics. 2020;181(6):2257-2303.
doi:10.1007/s10955-020-02663-4
apa: Maas, J., & Mielke, A. (2020). Modeling of chemical reaction systems with
detailed balance using gradient structures. Journal of Statistical Physics.
Springer Nature. https://doi.org/10.1007/s10955-020-02663-4
chicago: Maas, Jan, and Alexander Mielke. “Modeling of Chemical Reaction Systems
with Detailed Balance Using Gradient Structures.” Journal of Statistical Physics.
Springer Nature, 2020. https://doi.org/10.1007/s10955-020-02663-4.
ieee: J. Maas and A. Mielke, “Modeling of chemical reaction systems with detailed
balance using gradient structures,” Journal of Statistical Physics, vol.
181, no. 6. Springer Nature, pp. 2257–2303, 2020.
ista: Maas J, Mielke A. 2020. Modeling of chemical reaction systems with detailed
balance using gradient structures. Journal of Statistical Physics. 181(6), 2257–2303.
mla: Maas, Jan, and Alexander Mielke. “Modeling of Chemical Reaction Systems with
Detailed Balance Using Gradient Structures.” Journal of Statistical Physics,
vol. 181, no. 6, Springer Nature, 2020, pp. 2257–303, doi:10.1007/s10955-020-02663-4.
short: J. Maas, A. Mielke, Journal of Statistical Physics 181 (2020) 2257–2303.
corr_author: '1'
date_created: 2020-11-15T23:01:18Z
date_published: 2020-12-01T00:00:00Z
date_updated: 2025-06-12T07:01:39Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s10955-020-02663-4
ec_funded: 1
external_id:
arxiv:
- '2004.02831'
isi:
- '000587107200002'
pmid:
- '33268907'
file:
- access_level: open_access
checksum: bc2b63a90197b97cbc73eccada4639f5
content_type: application/pdf
creator: dernst
date_created: 2021-02-04T10:29:11Z
date_updated: 2021-02-04T10:29:11Z
file_id: '9087'
file_name: 2020_JourStatPhysics_Maas.pdf
file_size: 753596
relation: main_file
success: 1
file_date_updated: 2021-02-04T10:29:11Z
has_accepted_license: '1'
intvolume: ' 181'
isi: 1
issue: '6'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 2257-2303
pmid: 1
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 260482E2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: F06504
name: Taming Complexity in Partial Differential Systems
publication: Journal of Statistical Physics
publication_identifier:
eissn:
- 1572-9613
issn:
- 0022-4715
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Modeling of chemical reaction systems with detailed balance using gradient
structures
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 181
year: '2020'
...
---
_id: '6358'
abstract:
- lang: eng
text: We study dynamical optimal transport metrics between density matricesassociated
to symmetric Dirichlet forms on finite-dimensional C∗-algebras. Our settingcovers arbitrary skew-derivations and it provides a unified framework that simultaneously generalizes recently constructed transport metrics for Markov chains, Lindblad equations, and the Fermi Ornstein–Uhlenbeck semigroup. We develop a non-nommutative
differential calculus that allows us to obtain non-commutative Ricci curvature bounds, logarithmic Sobolev inequalities, transport-entropy inequalities, andspectral
gap estimates.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Eric A.
full_name: Carlen, Eric A.
last_name: Carlen
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
citation:
ama: Carlen EA, Maas J. Non-commutative calculus, optimal transport and functional
inequalities in dissipative quantum systems. Journal of Statistical Physics.
2020;178(2):319-378. doi:10.1007/s10955-019-02434-w
apa: Carlen, E. A., & Maas, J. (2020). Non-commutative calculus, optimal transport
and functional inequalities in dissipative quantum systems. Journal of Statistical
Physics. Springer Nature. https://doi.org/10.1007/s10955-019-02434-w
chicago: Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport
and Functional Inequalities in Dissipative Quantum Systems.” Journal of Statistical
Physics. Springer Nature, 2020. https://doi.org/10.1007/s10955-019-02434-w.
ieee: E. A. Carlen and J. Maas, “Non-commutative calculus, optimal transport and
functional inequalities in dissipative quantum systems,” Journal of Statistical
Physics, vol. 178, no. 2. Springer Nature, pp. 319–378, 2020.
ista: Carlen EA, Maas J. 2020. Non-commutative calculus, optimal transport and functional
inequalities in dissipative quantum systems. Journal of Statistical Physics.
178(2), 319–378.
mla: Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport
and Functional Inequalities in Dissipative Quantum Systems.” Journal of Statistical
Physics, vol. 178, no. 2, Springer Nature, 2020, pp. 319–78, doi:10.1007/s10955-019-02434-w.
short: E.A. Carlen, J. Maas, Journal of Statistical Physics 178 (2020) 319–378.
corr_author: '1'
date_created: 2019-04-30T07:34:18Z
date_published: 2020-01-01T00:00:00Z
date_updated: 2025-06-12T07:27:20Z
day: '01'
ddc:
- '500'
department:
- _id: JaMa
doi: 10.1007/s10955-019-02434-w
ec_funded: 1
external_id:
arxiv:
- '1811.04572'
isi:
- '000498933300001'
pmid:
- '33223567'
file:
- access_level: open_access
checksum: 7b04befbdc0d4982c0ee945d25d19872
content_type: application/pdf
creator: dernst
date_created: 2019-12-23T12:03:09Z
date_updated: 2020-07-14T12:47:28Z
file_id: '7209'
file_name: 2019_JourStatistPhysics_Carlen.pdf
file_size: 905538
relation: main_file
file_date_updated: 2020-07-14T12:47:28Z
has_accepted_license: '1'
intvolume: ' 178'
isi: 1
issue: '2'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 319-378
pmid: 1
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 260482E2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: F06504
name: Taming Complexity in Partial Differential Systems
publication: Journal of Statistical Physics
publication_identifier:
eissn:
- 1572-9613
issn:
- 0022-4715
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
link:
- relation: erratum
url: https://doi.org/10.1007/s10955-020-02671-4
scopus_import: '1'
status: public
title: Non-commutative calculus, optimal transport and functional inequalities in
dissipative quantum systems
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 178
year: '2020'
...
---
_id: '7573'
abstract:
- lang: eng
text: This paper deals with dynamical optimal transport metrics defined by spatial
discretisation of the Benamou–Benamou formula for the Kantorovich metric . Such
metrics appear naturally in discretisations of -gradient flow formulations for
dissipative PDE. However, it has recently been shown that these metrics do not
in general converge to , unless strong geometric constraints are imposed on the
discrete mesh. In this paper we prove that, in a 1-dimensional periodic setting,
discrete transport metrics converge to a limiting transport metric with a non-trivial
effective mobility. This mobility depends sensitively on the geometry of the mesh
and on the non-local mobility at the discrete level. Our result quantifies to
what extent discrete transport can make use of microstructure in the mesh to reduce
the cost of transport.
acknowledgement: J.M. gratefully acknowledges support by the European Research Council
(ERC) under the European Union's Horizon 2020 research and innovation programme
(grant agreement No 716117). J.M. and L.P. also acknowledge support from the Austrian
Science Fund (FWF), grants No F65 and W1245. E.K. gratefully acknowledges support
by the German Research Foundation through the Hausdorff Center for Mathematics and
the Collaborative Research Center 1060. P.G. is partially funded by the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation) – 350398276.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Peter
full_name: Gladbach, Peter
last_name: Gladbach
- first_name: Eva
full_name: Kopfer, Eva
last_name: Kopfer
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Lorenzo
full_name: Portinale, Lorenzo
id: 30AD2CBC-F248-11E8-B48F-1D18A9856A87
last_name: Portinale
citation:
ama: Gladbach P, Kopfer E, Maas J, Portinale L. Homogenisation of one-dimensional
discrete optimal transport. Journal de Mathematiques Pures et Appliquees.
2020;139(7):204-234. doi:10.1016/j.matpur.2020.02.008
apa: Gladbach, P., Kopfer, E., Maas, J., & Portinale, L. (2020). Homogenisation
of one-dimensional discrete optimal transport. Journal de Mathematiques Pures
et Appliquees. Elsevier. https://doi.org/10.1016/j.matpur.2020.02.008
chicago: Gladbach, Peter, Eva Kopfer, Jan Maas, and Lorenzo Portinale. “Homogenisation
of One-Dimensional Discrete Optimal Transport.” Journal de Mathematiques Pures
et Appliquees. Elsevier, 2020. https://doi.org/10.1016/j.matpur.2020.02.008.
ieee: P. Gladbach, E. Kopfer, J. Maas, and L. Portinale, “Homogenisation of one-dimensional
discrete optimal transport,” Journal de Mathematiques Pures et Appliquees,
vol. 139, no. 7. Elsevier, pp. 204–234, 2020.
ista: Gladbach P, Kopfer E, Maas J, Portinale L. 2020. Homogenisation of one-dimensional
discrete optimal transport. Journal de Mathematiques Pures et Appliquees. 139(7),
204–234.
mla: Gladbach, Peter, et al. “Homogenisation of One-Dimensional Discrete Optimal
Transport.” Journal de Mathematiques Pures et Appliquees, vol. 139, no.
7, Elsevier, 2020, pp. 204–34, doi:10.1016/j.matpur.2020.02.008.
short: P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Journal de Mathematiques Pures
et Appliquees 139 (2020) 204–234.
date_created: 2020-03-08T23:00:47Z
date_published: 2020-07-01T00:00:00Z
date_updated: 2026-04-08T07:00:03Z
day: '01'
department:
- _id: JaMa
doi: 10.1016/j.matpur.2020.02.008
ec_funded: 1
external_id:
arxiv:
- '1905.05757'
isi:
- '000539439400008'
intvolume: ' 139'
isi: 1
issue: '7'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1905.05757
month: '07'
oa: 1
oa_version: Preprint
page: 204-234
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 260482E2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: F06504
name: Taming Complexity in Partial Differential Systems
- _id: 260788DE-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: W1245
name: Dissipation and dispersion in nonlinear partial differential equations
publication: Journal de Mathematiques Pures et Appliquees
publication_identifier:
issn:
- 0021-7824
publication_status: published
publisher: Elsevier
quality_controlled: '1'
related_material:
record:
- id: '10030'
relation: dissertation_contains
status: public
scopus_import: '1'
status: public
title: Homogenisation of one-dimensional discrete optimal transport
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 139
year: '2020'
...
---
_id: '73'
abstract:
- lang: eng
text: We consider the space of probability measures on a discrete set X, endowed
with a dynamical optimal transport metric. Given two probability measures supported
in a subset Y⊆X, it is natural to ask whether they can be connected by a constant
speed geodesic with support in Y at all times. Our main result answers this question
affirmatively, under a suitable geometric condition on Y introduced in this paper.
The proof relies on an extension result for subsolutions to discrete Hamilton-Jacobi
equations, which is of independent interest.
article_number: '19'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Matthias
full_name: Erbar, Matthias
last_name: Erbar
- first_name: Jan
full_name: Maas, Jan
id: 4C5696CE-F248-11E8-B48F-1D18A9856A87
last_name: Maas
orcid: 0000-0002-0845-1338
- first_name: Melchior
full_name: Wirth, Melchior
last_name: Wirth
citation:
ama: Erbar M, Maas J, Wirth M. On the geometry of geodesics in discrete optimal
transport. Calculus of Variations and Partial Differential Equations. 2019;58(1).
doi:10.1007/s00526-018-1456-1
apa: Erbar, M., Maas, J., & Wirth, M. (2019). On the geometry of geodesics in
discrete optimal transport. Calculus of Variations and Partial Differential
Equations. Springer. https://doi.org/10.1007/s00526-018-1456-1
chicago: Erbar, Matthias, Jan Maas, and Melchior Wirth. “On the Geometry of Geodesics
in Discrete Optimal Transport.” Calculus of Variations and Partial Differential
Equations. Springer, 2019. https://doi.org/10.1007/s00526-018-1456-1.
ieee: M. Erbar, J. Maas, and M. Wirth, “On the geometry of geodesics in discrete
optimal transport,” Calculus of Variations and Partial Differential Equations,
vol. 58, no. 1. Springer, 2019.
ista: Erbar M, Maas J, Wirth M. 2019. On the geometry of geodesics in discrete optimal
transport. Calculus of Variations and Partial Differential Equations. 58(1), 19.
mla: Erbar, Matthias, et al. “On the Geometry of Geodesics in Discrete Optimal Transport.”
Calculus of Variations and Partial Differential Equations, vol. 58, no.
1, 19, Springer, 2019, doi:10.1007/s00526-018-1456-1.
short: M. Erbar, J. Maas, M. Wirth, Calculus of Variations and Partial Differential
Equations 58 (2019).
date_created: 2018-12-11T11:44:29Z
date_published: 2019-02-01T00:00:00Z
date_updated: 2026-04-16T09:51:42Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00526-018-1456-1
ec_funded: 1
external_id:
arxiv:
- '1805.06040'
isi:
- '000452849400001'
file:
- access_level: open_access
checksum: ba05ac2d69de4c58d2cd338b63512798
content_type: application/pdf
creator: dernst
date_created: 2019-01-28T15:37:11Z
date_updated: 2020-07-14T12:47:55Z
file_id: '5895'
file_name: 2018_Calculus_Erbar.pdf
file_size: 645565
relation: main_file
file_date_updated: 2020-07-14T12:47:55Z
has_accepted_license: '1'
intvolume: ' 58'
isi: 1
issue: '1'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
project:
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 260482E2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: F06504
name: Taming Complexity in Partial Differential Systems
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
publication: Calculus of Variations and Partial Differential Equations
publication_identifier:
issn:
- 0944-2669
publication_status: published
publisher: Springer
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the geometry of geodesics in discrete optimal transport
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: ba8df636-2132-11f1-aed0-ed93e2281fdd
volume: 58
year: '2019'
...