Probability as typicality

Volchan, Sérgio B.

doi:10.1016/j.shpsb.2006.12.001

Cited by 22 publications

(9 citation statements)

References 32 publications

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“…This is another way of understanding-how of thermodynamic processes. 26 Statistical mechanics gives us a deeper understanding for the same 25 There is a debate on whether one should rather interpret the measure as a typicality measure, but this should not concern us here (see, e.g., Volchan, 2007;Frigg, 2009;Werndl, 2013;Lazarovici and Reichert, 2015;Myrvold, 2019;Maudlin, 2020;Hubert, 2021). 26 One may think that because of the imaginary ensembles Gibbsian statistical mechanics (which is the most popular formulation among physicists) does not specify a mechanism-I thank an anonymous reviewer for raising this concern.…”

Section: Boltzmann Entropymentioning

confidence: 99%

Understanding physics: ‘What?’, ‘Why?’, and ‘How?’

Hubert

2021

Euro Jnl Phil Sci

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I want to combine two hitherto largely independent research projects, scientific understanding and mechanistic explanations. Understanding is not only achieved by answering why-questions, that is, by providing scientific explanations, but also by answering what-questions, that is, by providing what I call scientific descriptions. Based on this distinction, I develop three forms of understanding: understanding-what, understanding-why, and understanding-how. I argue that understanding-how is a particularly deep form of understanding, because it is based on mechanistic explanations, which answer why something happens in virtue of what it is made of. I apply the three forms of understanding to two case studies: first, to the historical development of thermodynamics and, second, to the differences between the Clausius and the Boltzmann entropy in explaining thermodynamic processes.

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Section: Boltzmann Entropymentioning

confidence: 99%

Understanding physics: ‘What?’, ‘Why?’, and ‘How?’

Hubert

2021

Euro Jnl Phil Sci

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“…This behavior can be phrased by means of typicality: a physical behavior is called typical, if almost all initial conditions yield this behavior (see, for instance, Goldstein, 2001;Lebowitz, 2008;Myrvold, 2016;Volchan, 2007). And a physical behavior is called atypical, if almost none of the initial conditions yield this behavior.…”

Section: Typicality and The Arrow Of Timementioning

confidence: 99%

“…4 There has been a long debate to make Boltzmann's argument more mathematically and conceptually precise. For our purpose, we do not need to dive into these details (see, e.g.,Volchan, 2007;Frigg, 2009;Werndl, 2013;Lazarovici and Reichert, 2015;Myrvold, 2019).…”

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confidence: 99%

Reviving Frequentism

Hubert

2021

Preprint

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Philosophers now seem to agree that frequentism is an untenable strategy to explain the meaning of probabilities. Nevertheless, I want to revive frequentism, and I will do so by grounding probabilities on typicality in the same way as the thermodynamic arrow of time can be grounded on typicality within statistical mechanics. This account, which I will call typicality frequentism, will evade the major criticisms raised against previous forms of frequentism. In this theory, probabilities arise within a physical theory from statistical behavior of almost all initial conditions. The main advantage of typicality frequentism is that it shows which kinds of probabilities (that also have empirical relevance) can be derived from physics. Although one cannot recover all probability talk in this account, this is rather a virtue than a vice, because it shows which types of probabilities can in fact arise from physics and which types need to be explained in different ways, thereby opening the path for a pluralistic account of probabilities.

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“…Elsewhere, we argued that a similar change was taking place, more or less at the same time, in Ludwig Boltzmann's statistical approach to kinetic gas theory. 36 Another interesting aspect of this story is the emergence of the singularities. Different kinds of singularities appear in many branches of physics ͑for example, in statistical mechanics, hydrodynamics, general relativity͒.…”

Section: Aftermath and Conclusionmentioning

confidence: 99%

Some insights from total collapse in the N-body problem

Volchan¹

2008

American Journal of Physics

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Simple, simpler, simplest: Spontaneous pattern formation in a commonplace system Am. J. Phys. 80, 578 (2012) Determination of contact angle from the maximum height of enlarged drops on solid surfaces Am. J. Phys. 80, 284 (2012) Aerodynamics in the classroom and at the ball park Am. J. Phys. 80, 289 (2012) The added mass of a spherical projectile Am.We discuss the Sundman-Weierstrass theorem of total collapse in its historical context. This remarkable and relatively simple result, a type of stability criterion, is at the crossroads of some interesting developments in the gravitational N-body problem. We use it as motivation to explore the connections to such important concepts as integrability, singularities, and typicality in order to gain insight into the transition from a predominantly quantitative to a novel qualitative approach to dynamical problems that took place at the end of the 19th century.

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Probability as typicality

Cited by 22 publications

References 32 publications

Understanding physics: ‘What?’, ‘Why?’, and ‘How?’

Understanding physics: ‘What?’, ‘Why?’, and ‘How?’

Reviving Frequentism

Some insights from total collapse in the N-body problem

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