What is thermodynamics? Most will answer this question by some variation of “thermodynamics is about the equilibrium state of matter.” But since Shannon took entropy outside physics the language of thermodynamics is popping up in all sort of places that have absolutely nothing to do with matter, places like networks, ecology and financial markets. The intuitive urge to use the language of thermodynamics so far away from its initial scope reflects a bolder principle: thermodynamics is a probabilistic calculus, a calculus for generic stochastic processes, of which Statistical Mechanics is just but one (albeit very important) example.
Under the heading Beyond Entropy I will be posting periodically my random thoughts on Entropy, Thermodynamics and Probability. The main ideas are gathered in my book Generalized Statistical Thermodynamics, though new refinements have emerged since its publication in 2018. As a historical note, this line of work was motivated by my interest in population balances, aggregation in particular, and its connection to statistical thermodynamics. Once this connection was established it became clear that that statistical thermodynamics is not specific to population balances per se, but rather to stochastic processes in general. The list of papers below offer the bibliography on this subject and is still evolving.
- T. Matsoukas. Stochastic Theory of Discrete Binary Fragmentation—Kinetics and Thermodynamics. Entropy 2022, 24(2), 229; DOI: 10.3390/e24020229
- T. Matsoukas. The Smoluchowski Ensemble – Statistical Mechanics of Aggregation. Entropy 2020, 21(9), 890 DOI: 10.3390/e22101181
- T. Matsoukas.Statistical Mechanics of Discrete Multicomponent Fragmentation. Condens. Matter 2020, 5(4), 64 DOI: 10.3390/condmat5040064
- T. Matsoukas. Thermodynamics and the evolution of stochastic populations, 2020 arXiv:2007.01362.
- T. Matsoukas. Thermodynamics Beyond Molecules: Statistical Thermodynamics of Probability Distributions, Entropy 2019, 21(9), 890; DOI:10.3390/e21090890
- T. Matsoukas. Generalized Statistical Thermodynamics: Thermodynamics of Probability Distributions and Stochastic Processes. Springer 2019. DOI:10.1007/978-3-030-04149-6
- T. Matsoukas. Statistical thermodynamics of clustered populations. Phys. Rev. E, 90:022113, Aug 2014, DOI:10.1103/PhysRevE.90.022113
- T. Matsoukas. Statistical thermodynamics of irreversible aggregation: The sol-gel transition. Sci. Rep., 5:8855, 2015, DOI:10.1038/srep08855
- T. Matsoukas. Thermodynamics of Irreversible Aggregation 2016. ECCOMAS 2016 (Heraklion, Greece). Manuscript available from ResearchGate.
- T. Matsoukas. Abrupt percolation in small equilibrated networks. Phys. Rev. E, 91:052105, May 2015, DOI:10.1103/PhysRevE.91.052105
