{
  "abstract": "Spatial temperature fields in Brownian heat engines are commonly prescribed \\emph{a priori}, and the resulting transport and thermodynamic properties are then calculated. Here we formulate the complementary inverse-design problem: determining the temperature profile and barrier height that optimize a chosen thermodynamic objective. We consider an overdamped Brownian particle in a symmetric triangular periodic potential under a constant opposing load and derive the exact stationary current and probability density for an arbitrary bounded temperature field, $\\Tc\\le T(x)\\le\\Th$. In the quasistatic limit, the efficiency becomes an exact functional of two inverse-temperature integrals over the uphill and downhill branches. Its rigorous global maximum under the pointwise temperature bounds is $η_{\\max}=1-\\Tc/\\Th$, attained uniquely, up to sets of measure zero, by the hot-uphill/cold-downhill piecewise-constant profile. At finite current, however, the optimization changes qualitatively because the current is determined jointly by the cycle affinity and a nonlocal transport resistance. We derive the exact functional gradient and the corresponding box-constrained optimality conditions, showing that the current- or power-maximizing profile generally differs from the quasistatic efficiency optimum. For any prescribed temperature field, the current-maximizing barrier satisfies an exact balance between the marginal gain in thermal rectification and the marginal increase in transport resistance, with the characteristic estimate $U_0^*\\simeq T_{\\rm act}$, where $T_{\\rm act}^{-1}=(2/L)\\int_0^{L/2}\\dd x/T(x)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02613",
  "author_total": 1,
  "authors": [
    {
      "name": "Mesfin Taye"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5qw6bgja40jpj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02613",
  "fulltext_url": null,
  "id": "5qw6bgja40jpj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02613",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "openalex",
      "3109|Advanced Thermodynamics and Statistical Mechanics"
    ]
  ],
  "openalex": "W7207702677",
  "pdf_url": "https://arxiv.org/pdf/2609.02613",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5qw6bgja40jpj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:16Z",
      "native_id": "2609.02613",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02613"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Thermodynamic optimization of thermal landscapes and energy barriers in a Brownian heat engine",
  "title_text": "Thermodynamic optimization of thermal landscapes and energy barriers in a Brownian heat engine",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:16Z",
  "url": "https://research.draconitic.com/paper/5qw6bgja40jpj",
  "venue": "arXiv",
  "versions": []
}