The First Law of Thermodynamics and the Abstraction to a Lack of Information in a Deterministic System Part 3 | Zenodo Skip to main Communities My dashboard Log in Sign up Published April 7, 2026 | Version v1 Preprint Open The First Law of Thermodynamics and the Abstraction to a Lack of Information in a Deterministic System Part 3 Authors/Creators Ruggeri, Francesco R. Description In Parts 1 and 2 and also in the first two references listed in Part 1, a deterministic system, namely a particle with pp/2m moving in a one-dimensional box, is analyzed using classical statistical mechanics. In particular, the second reference listed in Part 1 starts with the math equation d(pl) = l dp + p dl and multiplies it by (p/m) 1/l to establish the first law of thermodynamics to a deterministic system. Here we try to argue that a statistical treatment of such a classical system arises because one focuses on collective work, i,e. -Pressure dl. Pressure is due to the particle elastically bouncing off the walls and so the work becomes linked to the collective change dl and not dp (change in momentum). Ultimately, however, this is a Newtonian problem and so d (pp2/m) is due to the change dp, but in statistical mechanics, such a change is seen as dissipation or heat. Thus, classically one would write: d (pp2/m) = Force dl, with Force having nothing to do with pressure. In statistical mechanics, pressure seems to be the key idea. F=dp/dt = dp/dl v(ave) (Newtonian treatment) is not equivalent to P dl = (p/m) (1/l) dl. To take the statistical viewpoint seriously, one has to focus on the pressure, i.e. an average force on the wall with elastic collisions and treat the actual loss of pp/2m as linked to heat. We argue that ultimately the statistical view of the deterministic system yields d(pp/2m) with dl, the collective work not being of interest in the Newtonian picture. Thus, the statistical picture seems to be linked to the constraint l=constant more than any kind of random or probabilistic feature, we argue. Files physFirstLawDeterm3.pdf Files (90.1 kB) Name Size Download all physFirstLawDeterm3.pdf md5:3ab3d2eb06382f8fb38fad7b0a235ae9 90.1 kB Preview Download 24 Views 18 Downloads Show more details All versions This version Views Total views 24 24 Downloads Total downloads 18 18 Data volume Total data volume 1.7 MB 1.7 MB More info on how stats are collected.... Versions External resources Indexed in OpenAIRE Communities Details DOI DOI Badge DOI 10.5281/zenodo.19462066 Markdown [](https://doi.org/10.5281/zenodo.19462066) reStructuredText .. image:: https://zenodo.org/badge/DOI/10.5281/zenodo.19462066.svg :target: https://doi.org/10.5281/zenodo.19462066 HTML <a href="https://doi.org/10.5281/zenodo.19462066"><img src="https://zenodo.org/badge/DOI/10.5281/zenodo.19462066.svg" alt="DOI"></a> Image URL https://zenodo.org/badge/DOI/10.5281/zenodo.19462066.svg Target URL https://doi.org/10.5281/zenodo.19462066 Resource type Preprint Publisher Zenodo Rights License Creative Commons Attribution 4.0 International The Creative Commons Attribution license allows re-distribution and re-use of a licensed work on the condition that the creator is appropriately credited. Read more Citation Export Technical metadata Created April 7, 2026 Modified April 7, 2026 Jump up About About Policies Infrastructure Principles Projects Roadmap Contact Blog Blog Support Help FAQ Developers REST API OAI-PMH Contribute GitHub Donate Funded by Powered by CERN Data Centre & InvenioRDM Status Privacy policy Cookie policy Terms of Use This site uses cookies. Find out more on how we use cookies Accept all cookies Accept only essential cookies