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Carnot Cycle and Heat-Machines: From Applications (Systems and Processes) to Fundamentals (FDOT), Second Edition

A Special Issue of Entropy (ISSN 1099-4300) belonging to the section "Thermodynamics".

Deadline for manuscript submissions: 31 January 2027 | Viewed by 679

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Special Issue Information

Dear Colleagues,

Engineering thermodynamics has continued to improve since the sixties—one of the first advancements was the investigation of endoreversible direct and reverse machines. These phenomenological approaches are being improved, considering dissipative mechanisms, in order to represent more precisely the global performance of systems and processes (for example, cascades, combined heat and power, and the valorization of waste heat). 

The optimization of systems and processes requires defining clear objectives (simple or multiobjective optimization) and the constraints applied to the systems and processes. This is a general approach that can be summarized as FDOT (Finite Physical Dimensions Optimal Thermodynamics). Among these dimensions are the geometrical dimensions (size), but also time (Finite Time Thermodynamics, FTT). However, we can extend the approach to other dimensions, for example, with Finite Speed Thermodynamics (FST).

Efficiency could also be considered finite (for example, the effectiveness of Heat Exchangers (HEX)). Efficiency is a central concept that is multiform and generally non-dimensional. It is related to quality, and consequently to the second law of thermodynamics. When investigating efficiency we may consider economic concern, but also environmental concern, which is difficult to control nowadays.

Submissions are encouraged that discuss fundamental aspects of thermodynamics. This Special Issue is also open and connected to other branches of thermodynamics, mainly statistical thermodynamics and quantum thermodynamics—including a significant recent development regarding quantum machines. Research into all of these developments is welcomed, as well as entropy and exergy analysis. Connection to fundamental aspects also includes relativity in thermodynamics.

Prof. Dr. Michel Feidt
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • optimization
  • FDOT (Finite Physical Dimensions Optimal Thermodynamics)
  • least action principle (MAUPERTUIS)
  • finiteness principle (conjecture)
  • structure of the universe (large-scale)
  • FTT (Finite Time Thermodynamics)
  • FST (Finite Speed Thermodynamics)
  • efficiency
  • economy
  • environment
  • statistical thermodynamics
  • quantum thermodynamics
  • entropy analysis
  • exergy analysis

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Published Papers (1 paper)

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21 pages, 1752 KB  
Article
Finite-Time Thermodynamics of Battery Discharging: Power–Efficiency Trade-Off and Optimization
by Rui-Han Liu, Yun-Qian Lin and Yu-Han Ma
Entropy 2026, 28(8), 852; https://doi.org/10.3390/e28080852 - 30 Jul 2026
Viewed by 443
Abstract
Battery discharging is governed by a fundamental trade-off between output power and energy conversion efficiency due to internal dissipation. In this paper, we demonstrate that such a trade-off universally yields a parabolic envelope Pη(1η). The [...] Read more.
Battery discharging is governed by a fundamental trade-off between output power and energy conversion efficiency due to internal dissipation. In this paper, we demonstrate that such a trade-off universally yields a parabolic envelope Pη(1η). The efficiency at maximum power is exactly one half, mirroring the well-known half-Carnot limit in finite-time thermodynamics. To extend this bound into practical operational rules, we formulate a multistage constant-discharging (MSCD) schedule subject to simultaneous real-time load demands and a global discharging deadline. Analytical resolution via the Karush–Kuhn–Tucker conditions reveals a remarkably compact optimal policy: Ii=max(Iireq,I0). Under this rule, stages limited by external demand run exactly at their minimum required currents, while all remaining stages are elevated to a uniform baseline I0 fixed by the deadline constraint. By tracing the dissipation–time Pareto front, we quantify how internal resistance shifts the operational boundaries and sharpens the trade-off corner. This analysis establishes a rigorous thermodynamic baseline for the scheduling layer of battery management systems, offering natural extensions to nonlinear models incorporating temperature and state-of-charge dependencies. Full article
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