Asymmetry, Abstraction, and Autonomy: Justifying Coarse-Graining in Statistical Mechanics

Robertson, Katie

doi:10.1093/bjps/axy020

Cited by 20 publications

(39 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A recent philosophical discussion of this problem based on the Mori-Zwanzig projection operator method can be found in Ref. [40]. Moreover, it is discussed what precisely justifies the assumption of Markovian behavior [2].…”

Section: Mori-zwanzig Equation In a General Contextmentioning

confidence: 99%

Projection operators in statistical mechanics: a pedagogical approach

Vrugt

Wittkowski

2020

Eur. J. Phys.

View full text Add to dashboard Cite

The Mori-Zwanzig projection operator formalism is one of the central tools of nonequilibrium statistical mechanics, allowing to derive macroscopic equations of motion from the microscopic dynamics through a systematic coarse-graining procedure. It is important as a method in physical research and gives many insights into the general structure of nonequilibrium transport equations and the general procedure of microscopic derivations. Therefore, it is a valuable ingredient of basic and advanced courses in statistical mechanics. However, accessible introductions to this methodin particular in its more advanced forms -are extremely rare. In this article, we give a simple and systematic introduction to the Mori-Zwanzig formalism, which allows students to understand the methodology in the form it is used in current research. This includes both basic and modern versions of the theory. Moreover, we relate the formalism to more general aspects of statistical mechanics and quantum mechanics. Thereby, we explain how this method can be incorporated into a lecture course on statistical mechanics as a way to give a general introduction to the study of nonequilibrium systems. Applications, in particular to spin relaxation and dynamical density functional theory, are also discussed. * Corresponding author: raphael.wittkowski@uni-muenster.de 1 Active particles are particles that convert energy into directed motion. A good example are swimming microorganisms [1]. 2 This is not possible for active systems [7].

show abstract

Section: Mori-zwanzig Equation In a General Contextmentioning

confidence: 99%

Projection operators in statistical mechanics: a pedagogical approach

Vrugt

Wittkowski

2020

Eur. J. Phys.

View full text Add to dashboard Cite

show abstract

“…But coarse-graining is not a form of distortion, but rather irrelevant details are thrown away -and so this is a case of abstraction. (See Robertson (2019) for more details, and Myrvold (2014) for a similar line).…”

Section: Rapid Changesmentioning

confidence: 91%

In Search of the Holy Grail: How to Reduce the Second Law of Thermodynamics

Robertson¹

2022

The British Journal for the Philosophy of Science

Self Cite

View full text Add to dashboard Cite

Link to publication on Research at Birmingham portal General rightsUnless a licence is specified above, all rights (including copyright and moral rights) in this document are retained by the authors and/or the copyright holders. The express permission of the copyright holder must be obtained for any use of this material other than for purposes permitted by law.• Users may freely distribute the URL that is used to identify this publication.• Users may download and/or print one copy of the publication from the University of Birmingham research portal for the purpose of private study or non-commercial research.• User may use extracts from the document in line with the concept of 'fair dealing' under the Copyright, Designs and Patents Act 1988 (?) • Users may not further distribute the material nor use it for the purposes of commercial gain.Where a licence is displayed above, please note the terms and conditions of the licence govern your use of this document.When citing, please reference the published version. Take down policyWhile the University of Birmingham exercises care and attention in making items available there are rare occasions when an item has been uploaded in error or has been deemed to be commercially or otherwise sensitive.

show abstract

“…In statistical physics, the formulation of a pertinent phase space for a given kind of system, the assignment of probabilities to the different micro-states and macrostates of the system, and the selection of the criteria for the coarse-graining of the phase space are non-trivial tasks. They require background knowledge about some features of the causal structure of the target system and its laws of motion; they also require to choose a relevant set of observables and symmetries, which determine what properties of the system being modelled are preserved (or remain invariant) under some transformation (Español 2004;Robertson 2020).…”

Section: Phase Spaces In Biologymentioning

confidence: 99%

Non-equilibrium thermodynamics and the free energy principle in biology

Colombo

Palacios

2021

Biol Philos

View full text Add to dashboard Cite

According to the free energy principle, life is an “inevitable and emergent property of any (ergodic) random dynamical system at non-equilibrium steady state that possesses a Markov blanket” (Friston in J R Soc Interface 10(86):20130475, 2013). Formulating a principle for the life sciences in terms of concepts from statistical physics, such as random dynamical system, non-equilibrium steady state and ergodicity, places substantial constraints on the theoretical and empirical study of biological systems. Thus far, however, the physics foundations of the free energy principle have received hardly any attention. Here, we start to fill this gap and analyse some of the challenges raised by applications of statistical physics for modelling biological targets. Based on our analysis, we conclude that model-building grounded in the free energy principle exacerbates a trade-off between generality and realism, because of a fundamental mismatch between its physics assumptions and the properties of actual biological targets.

show abstract

Asymmetry, Abstraction, and Autonomy: Justifying Coarse-Graining in Statistical Mechanics

Cited by 20 publications

References 47 publications

Projection operators in statistical mechanics: a pedagogical approach

Projection operators in statistical mechanics: a pedagogical approach

In Search of the Holy Grail: How to Reduce the Second Law of Thermodynamics

Non-equilibrium thermodynamics and the free energy principle in biology

Contact Info

Product

Resources

About