Metraipolis › archive › dc_68858bf73bda

Reference-Measure Freedom of the Effective Hamiltonian: From Stochastic Thermodynamics to the Macroscopic Limit — arXiv:2609.38994

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.38994
License (as archived): CC0-1.0
Archived: 2026-10-07T15:49:06.907Z
SHA-256 of the archived text: 8c37d2365568b6e163796875fc557e8bee398e3f331b0fc025b9a5e1ad317d82
Stable URL of this page: https://metraipolis.com/documento/dc_68858bf73bda

How to cite

Reference-Measure Freedom of the Effective Hamiltonian: From Stochastic Thermodynamics to the Macroscopic Limit — arXiv:2609.38994 — arXiv (en), https://arxiv.org/abs/2609.38994 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_68858bf73bda (Metraipolis archive dc_68858bf73bda, sha256 8c37d2365568b6e163796875fc557e8bee398e3f331b0fc025b9a5e1ad317d82)

BibTeX

@misc{dc68858bf73bda,
  title = {Reference-Measure Freedom of the Effective Hamiltonian: From Stochastic Thermodynamics to the Macroscopic Limit — arXiv:2609.38994},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.38994},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_68858bf73bda; sha256 8c37d2365568b6e163796875fc557e8bee398e3f331b0fc025b9a5e1ad317d82},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.38994. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The effective Hamiltonian (EH), also referred to as the potential of mean force or free-energy landscape, is widely used to describe equilibrium properties and slow dynamics in chemical and softmatter systems. However, the conventional EH has been argued to be ill-defined because it does not transform as a scalar under a change of coordinates. Here, we show that this apparent problem originates from an implicit change of the reference measure (gauge) with respect to which the equilibrium probability density is defined. We formulate the equilibrium measure and the Fokker--Planck equation (FPE) intrinsically on the manifold of slow variables and show that an EH is a scalar function defined with respect to a chosen gauge. Different EHs, including the conventional EH and the diffusion-dependent EH recently proposed in a Riemannian formulation, thus provide different gauge representations of the same intrinsic equilibrium measure and stochastic dynamics. We further show that the gauge choice has an operational meaning: different restraint protocols for the slow variables select different reference measures. Finally, when the equilibrium measure obeys a large-deviation principle in a macroscopic limit, differences among EHs associated with subleading gauges become subleading relative to the large-deviation speed. The leading part of the EH is then determined by the gauge-independent large-deviation rate function, and the corresponding deterministic dynamics is likewise gauge independent.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-10-01 in cond-mat.stat-mech).
Categorie arXiv: Statistical Mechanics (cond-mat.stat-mech) ; Soft Condensed Matter (cond-mat.soft).
Pagina del lavoro: https://arxiv.org/abs/2609.38994 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T15:22:46.034Z dalla pagina https://arxiv.org/catchup/cond-mat.stat-mech/2026-10-01?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).