Usually, the deterministic part of our problem (the Hamiltonian or driving force) of our elements is not clearly defined.
The systems are, by far, smaller than the usual systems in statistical mechanics. So the statistical approach loses a lot of accuracy when compared with classical examples, with moles and moles of elements.
Despite these and other flaws, even such an oversimplified description is still an interesting approach to this kind of problems. In fact, statistical mechanics was the seed for the methods of the so-called complex systems science. Complex systems science is a subfield halfway between physics and applied mathematics, which evolved mostly (but not only) from statistical mechanics.
Currently, the field of complex systems covers an enormously wide range of applications in almost every field of knowledge (such as ecology 1, demography 2, economy 3 and, going back to our example of the raging crowd, even riot control 4 and law-enforcement 5).
W. Greiner, L. Neise, H. Stöcker. Thermodynamics and statistical mechanics. New York. Springer – Verlag. 1997. ISBN 978-1-4612-0827-3
J. Aguilar. Curso de termodinámica. Pearson Educación. ISBN 9788420513829.
1 Just for storing this data, assuming 2 bytes per number and 6 numbers per particle (position and momentum), will be required about 1016 Gb. This is roughly equivalent to 10.000 computers per person in the world. Not to talk about the horrible task of typing it all.
- Garcia-Algarra, Galeano, Pastor, Iriondo, Ramasco. Rethinking the logistic approach for population dynamics of mutualistic interactions. Journal of Theoretical Biology (2013). ArXiv ID: 1305.5411 ↩
- Castellano, Castellano, Fortunato et al. Statistical physics of social dynamics. Reviews of Modern Physics (2007). ArXiv ID: 0710.3256 ↩
- Yakovenko. (2012). Applications of statistical mechanics to economics: Entropic origin of the probability distributions of money, income, and energy consumption. ArXiv ID: 1204.6483. ↩
- Helbing, Johansson, Al-Abideen. Crowd turbulence: the physics of crowd disasters. (2007) ArXiv ID: 0708.3339 ↩
- D’Orsogna, Perc. Statistical physics of crime: A review. (2000). ArXiv ID: 1411.1743 ↩