The Logic of Thermostatistical Physics

Emch, Gérard G.; Liu, Chuang

doi:10.1007/978-3-662-04886-3

Cited by 74 publications

(45 citation statements)

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“…This model has been used extensively to study the Boltzmann H-theorem and to understand how the time asymmetry of diffusion processes arises from the underlying time symmetry in the laws of motion. 15,17,20 We use this model for a slightly different purpose. In particular, our aim is to take a well-characterized problem like diffusion and to reveal how the principle of maximum caliber may be used in a concrete way.…”

Section: Fick's Law From the Dog-flea Modelmentioning

confidence: 99%

“…To illustrate the principle, we use a slight variant of one of the oldest and simplest models in statistical mechanics, the dog-flea or two urn model. [15][16][17] Courses in dynamics often introduce Fick's law, Fourier's law, and the Newtonian-fluid model as phenomenological laws, rather than deriving them from some deeper foundation. We describe an unified perspective that we have found useful for teaching these laws from a foundation in statistical dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Teaching the principles of statistical dynamics

Ghosh

Dill

Inamdar

et al. 2006

American Journal of Physics

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We describe a simple framework for teaching the principles that underlie the dynamical laws of transport: Fick's law of diffusion, Fourier's law of heat flow, the Newtonian viscosity law, and the mass-action laws of chemical kinetics. In analogy with the way that the maximization of entropy over microstates leads to the Boltzmann distribution and predictions about equilibria, maximizing a quantity that E. T. Jaynes called "caliber" over all the possible microtrajectories leads to these dynamical laws. The principle of maximum caliber also leads to dynamical distribution functions that characterize the relative probabilities of different microtrajectories. A great source of recent interest in statistical dynamics has resulted from a new generation of single-particle and single-molecule experiments that make it possible to observe dynamics one trajectory at a time.

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Section: Fick's Law From the Dog-flea Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Teaching the principles of statistical dynamics

Ghosh

Dill

Inamdar

et al. 2006

American Journal of Physics

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“…In Section 5 we will return to question of the interpretations of idealization and consider a number of contemporary accounts. If we consider in particular the 1872 Boltzmann kinetic model (Boltzmann [1970], Emch and Liu [2002], Uffink [2014]) we can make a specific comparison between some of the key idealisations involved in income and gas kinetic exchange models. This list given in Table 1 is by no means meant to be exhaustive.…”

Section: Idealisations In Kinetic Exchange Modelsmentioning

confidence: 99%

Modelling Inequality

Thébault

Bradley

Reutlinger

2018

The British Journal for the Philosophy of Science

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Econophysics is a new and exciting cross-disciplinary research field that applies models and modelling techniques from statistical physics to economic systems. It is not, however, without its critics: prominent figures in more mainstream economic theory have criticised some elements of the methodology of econophysics. One of the main lines of criticism concerns the nature of the modelling assumptions and idealisations involved, and a particular target are 'kinetic exchange' approaches used to model the emergence of inequality within the distribution of individual monetary income. This paper will consider such models in detail, and assess the warrant of the criticisms drawing upon the philosophical literature on modelling and idealisation. Our aim is to provide the first steps towards informed mediation of this important and interesting interdisciplinary debate, and our hope is to offer guidance with regard to both the practice of modelling inequality, and the inequality of modelling practice.

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“…The conversion of mechanical work into heat is a famous topic of such studies. His works, although also very controversial at the beginning, were seminal and yielded the 1st law of Thermodynamics, see, e.g., [4]. Recall also that all mechanical work can be converted to heat but the converse is not true, in general.…”

Section: The Genesis Of Ohm and Joule's Lawsmentioning

confidence: 99%

Microscopic foundations of Ohm and Joule's laws – The relevance of thermodynamics

Bru¹,

Pedra²

2014

Mathematical Results in Quantum Mechanics

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We give a brief historical account on microscopic explanations of electrical conduction. One aim of this short review is to show that Thermodynamics is fundamental to the theoretical understanding of the phenomenon. We discuss how the 2nd law, implemented in the scope of Quantum Statistical Mechanics, can be naturally used to give mathematical sense to conductivity of very general quantum many-body models. This is reminiscent of original ideas of J.P. Joule. We start with Ohm and Joule's discoveries and proceed by describing the Drude model of conductivity. The impact of Quantum Mechanics and the Anderson model are also discussed. The exposition is closed with the presentation of our approach to electrical conductivity based on the 2nd law of Thermodynamics as passivity of systems at thermal equilibrium. It led to new rigorous results on linear conductivity of interacting fermions. One example is the existence of so-called AC-conductivity measures for such a physical system. These measures are, moreover, Fourier transforms of time correlations of current fluctuations in the system. I.e., the conductivity satisfies, for a large class of quantum mechanical microscopic models, Green-Kubo relations.

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The Logic of Thermostatistical Physics

Abstract: The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Cited by 74 publications

References 0 publications

Teaching the principles of statistical dynamics

Teaching the principles of statistical dynamics

Modelling Inequality

Microscopic foundations of Ohm and Joule's laws – The relevance of thermodynamics

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