Minimal Information versus Stochasticity in an Ideal Gas
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2025
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| _version_ | 1866901481579347968 |
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| author | Ruggeri, Francesco Rocco |
| author_facet | Ruggeri, Francesco Rocco |
| contents | <p>Classical statistical mechanics of an ideal gas is usually described as applying to a system consisting of a very large number of particles (10 power 23) for which one cannot practically track all trajectories. Furthermore , such a system is said to be described by single parameters such as volume V, pressure P, and temperature T. In the case of an ideal gas, one has PV=nRT, so that dE= -PdV (no heat flow) means that -PdV= nRT d ln(1/V). Here 1/V is a probability, and ln(1/V) information in information theory. These notions seem to be directly related to the statistical gas, but we argue that they appear for a deterministic system of a few particles. </p> <p> We consider first the case of a deterministic single particle in a one dimensional box and then a small number of deterministic single particles to see how a constant P is directly linked to uniform distribution in the volume, even for a deterministic system. The uniform distribution suggests a minimal amount of information as well as a constant P (averaged over a small time) and so the stochasticity seems to be related to finding a particular single particle at any given point x. If one thinks in terms of identical particles, then a uniform distribution in x does not seem to be linked to stochasticity. Thus, the stochasticity seems to be related to the Newtonian idea of identifying each particle.</p> <p> Given that d ln(1/V) appears for a small number of deterministic particles, it seems to be linked to the fact that one wishes to have the deterministic system describe a constant P instead of P(t) which means that one has minimized information. This, in turn, is associated with a uniform distribution in space (again minimal information), but there does not seem to be stochasticity in the deterministic example using a few particles.</p> <p> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_14604887 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
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| spellingShingle | Minimal Information versus Stochasticity in an Ideal Gas Ruggeri, Francesco Rocco <p>Classical statistical mechanics of an ideal gas is usually described as applying to a system consisting of a very large number of particles (10 power 23) for which one cannot practically track all trajectories. Furthermore , such a system is said to be described by single parameters such as volume V, pressure P, and temperature T. In the case of an ideal gas, one has PV=nRT, so that dE= -PdV (no heat flow) means that -PdV= nRT d ln(1/V). Here 1/V is a probability, and ln(1/V) information in information theory. These notions seem to be directly related to the statistical gas, but we argue that they appear for a deterministic system of a few particles. </p> <p> We consider first the case of a deterministic single particle in a one dimensional box and then a small number of deterministic single particles to see how a constant P is directly linked to uniform distribution in the volume, even for a deterministic system. The uniform distribution suggests a minimal amount of information as well as a constant P (averaged over a small time) and so the stochasticity seems to be related to finding a particular single particle at any given point x. If one thinks in terms of identical particles, then a uniform distribution in x does not seem to be linked to stochasticity. Thus, the stochasticity seems to be related to the Newtonian idea of identifying each particle.</p> <p> Given that d ln(1/V) appears for a small number of deterministic particles, it seems to be linked to the fact that one wishes to have the deterministic system describe a constant P instead of P(t) which means that one has minimized information. This, in turn, is associated with a uniform distribution in space (again minimal information), but there does not seem to be stochasticity in the deterministic example using a few particles.</p> <p> </p> |
| title | Minimal Information versus Stochasticity in an Ideal Gas |
| url | https://doi.org/10.5281/zenodo.14604887 |