Thermodynamic Hamiltonian and Entropy Production
Abstract
1. Introduction
2. Materials and Methods
2.1. The System Considered
- 1.
- , : The set is called the set of the states accessible from σ, and consequently, it is the entire state space, the phase space Ω;
- 2.
- If and .
- 1.
- ;
- 2.
- ;
- 3.
- .
- 1.
- ;
- 2.
- The algebra is closed under countable intersections and subtraction of sets;
- 3.
- If k ≡ {∞} then is said to be a σ-algebra.
- 1.
- ;
- 2.
- If and ;
- 3.
- If and .
- 1.
- Covariant: . This means that the tangent planes to the coordinate surface at σ are mapped over the corresponding planes at ;
- 2.
- Continuous: , with , depends continuously on σ;
- 3.
- Transitivity: There is a point in a subsystem of of zero Liouville probability, called an attractor, with a dense orbit.
2.2. Thermodynamic Lagrangian and Entropy Generation
3. Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
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Lucia, U.; Grisolia, G. Thermodynamic Hamiltonian and Entropy Production. Mathematics 2025, 13, 3214. https://doi.org/10.3390/math13193214
Lucia U, Grisolia G. Thermodynamic Hamiltonian and Entropy Production. Mathematics. 2025; 13(19):3214. https://doi.org/10.3390/math13193214
Chicago/Turabian StyleLucia, Umberto, and Giulia Grisolia. 2025. "Thermodynamic Hamiltonian and Entropy Production" Mathematics 13, no. 19: 3214. https://doi.org/10.3390/math13193214
APA StyleLucia, U., & Grisolia, G. (2025). Thermodynamic Hamiltonian and Entropy Production. Mathematics, 13(19), 3214. https://doi.org/10.3390/math13193214

