Test of Information Theory on the Boltzmann Equation

The two-dimensional steady-state Boltzmann equation for hard-disk molecules in the presence of a temperature gradient has been solved explicitly to second order in density and the temperature gradient. The two-dimensional equation of state and some physical quantities are calculated from it and compared with those for the two-dimensional steady-state Bhatnagar-Gross-Krook(BGK) equation and information theory. We have found that the same kind of qualitative differences as the ...

Lecture given at the International Meeting ``Boltzmann's Legacy - 150 Years after his Birth'', organized by the Accademia Nazionale dei Lincei, 25 - 28 May 1994, in Rome, to be published in: ``Atti dell"Accademia Nazionale dei Lincei'', 1997.

To test kinetic theories, simple and practical setups are proposed. It turns out that these setups cannot be treated by Boltzmann's equation. An alternative method, called the path-integral approach, is then employed and a number of ready-for-verification results are obtained.

In this study, we present a reformulation of classical equilibrium thermodynamics by replacing the obscure and ambiguous concept of entropy with the clear and intuitive concept of information stored in a thermodynamic system. Specifically, we rewrite the laws of thermodynamics in the mathematical terminology borrowed from information theory with an emphasis on information instead of entropy and on binary logarithm instead of natural one. We also define a modified ideal gas co...

Starting from microscopic mechanics, we derive thermodynamic relations for heat conducting nonequilibrium steady states. The extended Clausius relation enables one to experimentally determine nonequilibrium entropy to the second order in the heat current. The associated Shannon-like microscopic expression of the entropy is suggestive. When the heat current is fixed, the extended Gibbs relation provides a unified treatment of thermodynamic forces in linear nonequilibrium regim...

This is a short note for some basics of information geometry from thermodynamics and Callen's themostatistics.

In the last quarter of the nineteenth century, Ludwig Boltzmann explained how irreversible macroscopic laws, in particular the second law of thermodynamics, originate in the time-reversible laws of microscopic physics. Boltzmann's analysis, the essence of which I shall review here, is basically correct. The most famous criticisms of Boltzmann's later work on the subject have little merit. Most twentieth century innovations -- such as the identification of the state of a physi...

It will be shown, how the Boltzmannian ideas on statistical physics can be naturally applied to nonequilibrium thermodynamics. A similar approach for treating nonequilibrium phenomena has been successfully used by Einstein and Smoluchowski treating fluctuations. It will be argued, that due to the reversibility of the microscopic equations, all processes - also macroscopic ones - must at least in principle be reversible. Also, a clear conceptual distinction between equilibrium...

The paper moves a step towards the full integration of statistical mechanics and information theory. Starting from the assumption that the thermodynamical system is composed by particles whose quantized energies can be modelled as independent and identically distributed random variables, the paper proposes an approach whose cornerstones are the information-theoretic typical set and the conditional equiprobability of microstates given certain macrostates of the system. When ta...

Using information entropy formalism, we consider a one-dimensional system with heat flux and extend the meaning of equilibrium variables to non equilibrium scenarios when classical local equilibrium approach is not applicable; this is particularly important for the performance evaluation of modern thermal systems and microdevices, which usually operate in extreme situations. The extended non equilibrium entropy, temperature, thermal conductivity and heat capacity have been an...