Proposed Lorentz Center workshop · Target: spring 2027
Towards independent assessment of a proposed general method for reversible-cycle benchmarking.
We are developing a proposed Lorentz Center workshop to investigate whether the established Clausius reversible-cycle equality can be operationalized into a general, explicitly qualified method for benchmarking thermodynamic cycles with both isothermal and non-isothermal heat exchange.
The intended programme brings together thermodynamic science and engineering with relevant perspectives from physics and astronomy, to examine the proposed method independently, compare it with existing treatments and establish its scope, limitations and possible implications.
Carnot provides the exact classical reversible benchmark for cyclic heat–work conversion between two constant-temperature reservoirs. The Clausius reversible-cycle equality also applies when reversible heat exchange occurs over varying temperatures:
These are established foundations of thermodynamics.
The proposed contribution concerns their operational use. It combines the Clausius equality with energy balance and specified heat-exchange trajectories to construct process-specific reversible-cycle benchmarks, subject to explicit assumptions and qualification conditions.
The two expressions below use heat-engine efficiency and heating or refrigeration COP as familiar examples of target quantities. The first refers to the Carnot reversible-isothermal cycle equality; the second refers to the Clausius reversible-cycle equality, which also covers non-isothermal heat exchange. These performance measures illustrate the proposed operational approach; they do not exhaust its scope.
Established two-isothermal case
For reversible cyclic operation with heat supplied and removed at two constant temperatures, this balance, together with energy balance, yields the familiar Carnot efficiency and COP relations.
Proposed general operationalization
The proposed method operationalizes the established Clausius reversible-cycle equality to determine a qualified, process-specific reversible efficiency or COP for specified heat-exchange trajectories. It includes non-isothermal configurations and retains the two-isothermal case as a special case.
The proposed modernization of thermodynamic cycle theory is broader than deriving performance ratios. Formal Core organizes the method around different selections of known data, target quantities and configuration variables. The question can therefore shift from “What is the reversible efficiency or COP?” to “Which heat quantity, boundary temperature or work quantity is consistent with this specified reversible-cycle benchmark?”
Within the two-isothermal domain, the Carnot equality supports alternative solve-for relations for heat quantities and boundary temperatures. Together with the First-Law cycle balance and the relevant definitions, it also supports work, efficiency and COP calculations. The proposed Clausius operationalization extends this logic to discrete, continuous and mixed heat–temperature representations, including the determination of unresolved configuration variables or trajectory parameters.
Which quantities can be determined depends on the information supplied and the complete set of governing constraints. Sufficient closure and physical admissibility are essential. Where these do not select a unique solution, the result must remain an admissible solution set or an explicitly underdetermined problem. This configurable approach is the broader methodological contribution described in Formal Core, available for review on request.
Can this operationalization provide a general, useful method for deriving process-specific reversible-cycle benchmarks across different cycle configurations?
Potential significance · Subject to independent assessment
The proposed modernization can be understood in two markedly different ways. At its most modest, it is “merely” a further mathematical operationalization of the Clausius relation of 1865: making established thermodynamic knowledge explicit, systematic and practically applicable, without introducing a new law of nature.
At its most ambitious, if the claimed scope and added value withstand independent scrutiny, the same operationalization could bring a profound modernization of how thermodynamic cycle theory is organized, taught and applied. The significance would lie in what a fully operational framework enables across cycle configurations, scientific disciplines and engineering applications.
The proposed operationalization aims to organize established reversible-cycle relations into a systematic framework for selecting known data, determining target quantities and constructing qualified, process-specific benchmarks. If independently validated, it could help researchers make assumptions explicit, compare cycle configurations and examine heat–work interactions within a common methodological structure.
Its potential scientific relevance extends beyond engineering applications to selected questions in materials science, physics, Earth sciences and astronomy. Applicability depends on whether a meaningful thermodynamic cycle can be defined and whether the system and processes satisfy the method’s scope and assumptions. Scientific assessment of that relevance provides the basis for any subsequent changes to teaching and professional practice.
Textbooks and technical references help shape lecture notes, course content and worked examples in universities and higher technical education. Through these materials, students learn which thermodynamic models to use, which assumptions to check and which benchmarks to select when assessing a cycle.
These choices carry into professional practice. The way cycle theory is taught influences how engineers formulate problems, interpret calculations and judge opportunities for improvement. Continuing education, engineering software and technical guidance can further transmit and reinforce those approaches.
If independently validated, the proposed modernization could strengthen this chain by giving the Carnot special case, non-isothermal cycles and process-specific reversible benchmarks a more explicit and systematic place in teaching. The educational value would lie in helping future engineers select and apply the appropriate benchmark for the actual question.
Benchmark selection helps determine what engineers regard as a performance limit, which losses they investigate and where they direct optimization efforts. This connects the treatment of cycle theory in education to the design, modelling and operation of combustion engines, power plants, heat pumps, refrigeration systems and other thermal installations.
For design decisions, this could help engineers assess whether to improve thermal matching, adjust heat-exchange trajectories or reconsider the cycle configuration. Within a defined comparison class, process-specific benchmarks could help distinguish configuration limits from potentially avoidable losses and guide which alternatives deserve detailed modelling or testing. The practical value would lie in directing optimization efforts towards physically justified opportunities and making the assumptions behind design choices explicit.
Where that leads to technically and economically feasible changes, the result may be lower fuel or electricity consumption for the required service. This is a pathway through which improved methods could support energy efficiency and sustainability; the achievable gains depend on the application, implementation and operating conditions and must be demonstrated in practice.
The stakes extend well beyond a single formula. If the proposed operationalization withstands independent scrutiny, its implications could reach how thermodynamic cycles are explained, compared and taught across science and engineering.
Our educational and publishing evidence report maps that potential reach across 20 publisher groups and 34 disciplines. It identifies 678 work families with evidence supporting targeted review, should Formal Core be independently validated. The relevance extends from foundational textbooks to specialist engineering references.
That scale deserves a serious scientific response. If the method offers a substantive advance, teaching and reference literature should reflect it. If established approaches already provide an equivalent framework, that should be demonstrated just as clearly. Either outcome calls for rigorous examination of the derivations, existing knowledge and representative applications.
This is why the proposed workshop matters: to bring independent researchers, educators and publishers together around a question with potentially far-reaching consequences. The report establishes a case for review—not a finding that books are wrong or that the proposed method has already been validated.
The supporting report, Potential Educational and Publishing Relevance of Beyond Carnot: Operationalizing Clausius, is available on request through Research Documents.
Leiden, the Netherlands
The Lorentz Center is an international scientific workshop centre based at Leiden University and structurally supported by both Leiden University and the Dutch Research Council (NWO). It brings researchers from around the world together to explore important open questions, examine emerging ideas and develop new research directions.
Its scope encompasses the natural, social and medical sciences, the humanities, and the interfaces between them. Lorentz Center describes this openness to all disciplines and their intersections as a globally distinctive feature: researchers can bring together precisely the combination of expertise that a scientific question requires. Institutional background
The centre combines high scientific standards with an explicit openness to daring initiatives. This creates room for ambitious, exploratory work whose outcomes remain uncertain, but whose potential scientific value merits serious investigation. Its mission emphasizes scientific quality, diverse perspectives and connections between academia, society and industry.
Lorentz Center pursues these aims through focused scientific workshops: international working meetings, typically lasting five days, built around intensive discussion, collaborative work and informal exchange. This sustained interaction gives participants time to examine assumptions, challenge interpretations and work through questions together.
Scientific coordinators and advisory boards help organizers shape the programme, while the centre provides practical and scientific support. The format brings complementary expertise into direct dialogue and helps participants identify concrete next steps for research. The workshop format
For Beyond Carnot: Operationalizing Clausius, we see this combination of scientific ambition, complementary expertise and sustained interaction as particularly valuable for independently assessing the proposed method, its limitations and its potential implications for thermodynamic cycle theory.
A draft workshop proposal has been prepared for consideration in the Lorentz Center programme. We are further developing the scientific programme and organizing team and working on preparations for the proposed workshop in spring 2027. This remains the target period, subject to formal acceptance and confirmation of workshop dates.
Programme under development
01
Identify relevant prior work and clarify the relationship to established Carnot and Clausius analysis, entropy and exergy methods, Lorenz-cycle and finite-reservoir treatments. Determine whether substantially equivalent methods already resolve the central question.
02
Examine the derivations independently. Make assumptions, boundary conditions and required input information explicit. Investigate potential counterexamples, ambiguous cases and limits of applicability.
03
Apply the proposed method and relevant existing methods to selected isothermal and non-isothermal cycle configurations. Distinguish conversion performance from reversibility and examine which comparisons are physically meaningful.
04
Determine which conclusions are supported and what remains unresolved. Consider possible consequences for engineering analysis, education and scientific literature, together with further numerical or experimental assessment where required.
The intended outcome is a documented scientific assessment: points of agreement and disagreement, demonstrated capabilities and limitations, and clearly formulated follow-up questions.
Thermodynamics provides a common framework across engineering and several branches of the physical sciences. The proposed workshop connects two complementary areas of expertise.
Expertise in thermodynamic cycles, reversible benchmarks, non-isothermal heat exchange, energy and exergy analysis, and computational methods is central to assessing the proposal.
Relevant application areas include heat engines, power generation, combustion engines, heat pumps and refrigeration. Contributions may include established comparison methods, representative cycle cases, numerical reconstruction and critical examination of the proposed framework.
Contributions from physics and astronomy can strengthen the examination of thermodynamic assumptions, theoretical consistency and applicability to selected physical systems.
Relevance must be established for each case: whether a meaningful cycle can be defined, how heat and work interactions are specified, and whether the required thermodynamic conditions are satisfied. Applicability to a natural or astrophysical system is a question to investigate.
The organizing team and prospective participant group are in development. We welcome exploratory discussions with researchers who can contribute subject expertise, independent scrutiny, programme development or relevant comparison cases.
Potential contributions include reviewing the scientific question, helping shape the programme, identifying prior work, reconstructing derivations and proposing cases that test the method’s boundaries.
Industrial researchers and engineers may contribute application questions, modelling expertise and suitable comparison cases. Possible performance improvements remain application-dependent and require substantiation.
Educators, textbook authors and academic publishers may contribute perspectives on the presentation of reversible benchmarks, cycle theory and non-isothermal heat exchange. They can help secure access to the priority chapters identified in the evidence report and assess representative teaching cases. Editorial decisions and proposed changes to teaching or literature should follow independent scientific assessment.
Organizations interested in supporting the initiative are invited to discuss possible arrangements. The availability and form of sponsorship acknowledgement or other visibility would need to be agreed with the relevant parties. Scientific conclusions must remain independent of financial support.
The introductory presentation, From a Specific Formula to a General Method, uses the square–rectangle analogy to explain the proposed Carnot–Clausius relationship and the purpose of independent assessment.
Dutch and English PDF editions are available for direct download. The draft workshop proposal describes the intended scientific scope and programme and can be requested separately. Formal Core review access has its own application route.
Tell us about your expertise, your interest in the scientific question and the contribution you would like to discuss. An expression of interest starts a conversation; participation and other arrangements will be confirmed separately.
To receive the proposal, use the workshop-proposal request form. You can describe your interest there; a second contact message is not needed.