Contributions to the Theory of Thermostated Systems II: Least Dissipation of Helmholtz Free Energy in Nano-Biology

In this paper, we develop further the theory of thermostated systems along the lines of our earlier paper. Two results are highlighted: 1) in the Markov limit of the contracted description, a least dissipation of Helmholtz free energy principle is established; and 2) a detailed account of the appropriateness of this principle for nano-biology, including the evolution of life, is presented.

💡 Research Summary

The paper extends the authors’ earlier work on thermostated systems by focusing on the Markov limit of a contracted description and establishing a “least dissipation of Helmholtz free energy” (LDHFE) principle. The authors begin by recalling that a full thermostated system can be described by high‑dimensional Langevin dynamics, where fast degrees of freedom act as a Gaussian heat bath. By averaging over these fast variables they obtain a reduced, low‑dimensional stochastic dynamics that obeys a Fokker‑Planck equation. In the Markov limit the transition probability kernel (K(x!\to!x’;\Delta t)) satisfies a detailed‑balance condition with respect to the Helmholtz free‑energy landscape (F(x)).

The central theoretical result is a variational principle: among all admissible paths (\gamma) connecting an initial state to a final state over a time interval (