Scientific foundations · Engineering and applications
Maximum COP and heat engine efficiency beyond isothermal reservoirs
A critical review of reversible benchmarks for heat pumps, refrigeration and heat engines
SCIENTIFIC REVIEW MANUSCRIPT · AVAILABLE ON REQUESTWhich methods does the scientific literature provide for reversible heat-engine efficiency and heat-pump and refrigeration COP benchmarks beyond the two-isothermal case, and how do they compare with the proposed parent reversible-cycle benchmark framework based on complete operationalization of the Clausius reversible-cycle equality? This review examines their scope, overlap and differences, and the evidence for any additional operational contribution of the proposed framework.
Why maximum COP and engine efficiency matter
A well-defined maximum COP or engine efficiency provides a physical reference for judging actual performance under specified thermal conditions and constraints. It helps make comparisons meaningful, distinguish thermodynamic limits from implementation losses, and identify improvement potential. This can guide working-fluid selection, Thermal Matching, component improvements and cycle redesign.
The gap to a reversible reference is not automatically a technically or economically recoverable gain. Maximum efficiency or COP must also be distinguished from maximum power. These practical purposes motivate the review’s comparison of benchmark methods.
What the review examines
The bibliography contains 77 references: 70 external bibliographic sources and seven proposal, author-analysis or framing documents. The external sources include scientific journal articles, conference contributions, theses, research reports and supporting technical material. Each reference identifies a source, not necessarily a distinct method or an independent validation. The depth of assessment varies with the material available.
This is a comparison of methods in scientific and technical literature, distinct from the programme’s separate assessment of thermodynamics textbooks and their potential need for revision. The review distinguishes 16 partly overlapping approaches, encompassing established benchmarks, optimization procedures and performance estimates—not sixteen independent exact reversible-limit methods.
The review recognizes substantial established capability beyond the classical two-isothermal Carnot formulas, including finite-stream Lorenz and entropic-temperature references, exergy-based constructions, variable-temperature reversible-work calculations, general multiple-reservoir work relations and cycle-specific procedures.
The comparison examines the problems each approach addresses, its required inputs and constraints, and how it handles benchmark determination and qualification. It considers changing heat-exchange temperatures, alternative choices of known and unknown variables, and configurations that may be infeasible, underdetermined or non-unique.
Comparison with the proposed parent reversible cycle benchmark framework
The proposed parent reversible-cycle benchmark framework is a subject of comparison in this review, rather than the method being introduced or taught by this publication. Its scientific and methodological specification is provided separately in the Formal Core Specification. The review asks where identified methods overlap with that framework, where their problem definitions or procedures differ, and what evidence would be needed to establish additional value.
Selected analytical comparisons identify consistency and overlap with earlier methods. Meaningful comparisons require the same physical boundaries, fixed data, constraints and objectives; different numerical results do not by themselves establish a superior method. A reversible result must also be distinguished from a demonstrated maximum over a specified comparison class.
Within the reviewed evidence, no single broadly accepted operational architecture is demonstrated to cover the full declared problem domain. This is a bounded literature finding—not a claim that non-isothermal benchmark methods are absent or a measurement of scientific community consensus. Completeness, full procedural equivalence, novelty and independent validation of the proposed framework remain open to assessment. Programme-connected documents provide comparison material, not independent validation.
Request the manuscript
For thermodynamics researchers, engineers, lecturers and scientific reviewers. Requests are assessed individually, with provision handled separately. The manuscript is not publicly downloadable and is not automatically attached to the acknowledgement. Requesting it does not grant access to the Formal Core.