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We derive general trade-off relations among the power, efficiency, and constancy for two-terminal thermoelectric systems in the linear response regime. Constancy, which quantifies the steadiness of the heat engine, is measured by its…

Statistical Mechanics · Physics 2026-04-09 Ousi Pan , Zhiqiang Fan , Shunjie Zhang , Liwei Chen , Jincan Chen , Shanhe Su

Carnot established in 1824 that the efficiency of cyclic engines operating between a hot bath at absolute temperature $T_{hot}$ and a bath at a lower temperature $T_{cold}$ cannot exceed $1-T_{cold}/T_{hot}$. We show that linear oscillators…

Physics Education · Physics 2016-09-08 J. Arnaud , L. Chusseau , F. Philippe

The efficiency of macroscopic heat engines is restricted by the second law of thermodynamics. They can reach at most the efficiency of a Carnot engine. In contrast, heat currents in mesoscopic heat engines show fluctuations. Thus, there is…

Mesoscale and Nanoscale Physics · Physics 2015-09-23 Sebastian Pilgram , David Sanchez , Rosa Lopez

The availability of controllable macroscopic devices, which maintain quantum coherence over relatively long time intervals, for the first time allows an experimental realization of many effects previously considered only as…

Quantum Physics · Physics 2014-08-05 A. M. Zagoskin , S. Savel'ev , Franco Nori , F. V. Kusmartsev

We study the optimal performance of an endoreversible quantum dot heat engine, in which the heat transfer between the system and baths is mediated by qubits, operating under the conditions of a trade-off objective function known as maximum…

Statistical Mechanics · Physics 2023-01-11 Kirandeep Kaur , Anmol Jain , Love Sahajbir Singh , Rakesh Singla , Shishram Rebari

The efficiency at maximum power has been investigated extensively, yet the practical control scheme to achieve it remains elusive. We fill such gap with a stepwise Carnot-like cycle, which consists the discrete isothermal process (DIP) and…

Quantum Physics · Physics 2018-08-29 Yu-Han Ma , Dazhi Xu , Hui Dong , Chang-Pu Sun

In systems described by the scattering theory, there is an upper bound, lower than Carnot, on the efficiency of steady-state heat to work conversion at a given output power. We show that interacting systems can overcome such bound and…

Statistical Mechanics · Physics 2018-08-27 Rongxiang Luo , Giuliano Benenti , Giulio Casati , Jiao Wang

Stability is an important property of small thermal machines with fluctuating power output. We here consider a finite-time quantum Carnot engine based on a degenerate multilevel system and study the influence of its finite Hilbert space…

Statistical Mechanics · Physics 2021-08-18 Tobias Denzler , Eric Lutz

From the steam engine to current nano-devices, the design of efficient thermal machines has been instrumental in modern societies. In its essence a thermal engine can be thought as a working substance, in contact with two or more baths,…

Statistical Mechanics · Physics 2016-03-18 Michele Campisi , Rosario Fazio

From thermodynamics point of view, in this era of aiming at energy conservation and sustainability, we need to develop more accurate ways to design thermal power, cooling and heat pump cycles. It has been the general practice in…

Statistical Mechanics · Physics 2013-07-23 GA Mansoori

We study the efficiency at maximum power of non-adiabatic dissipative (internally dissipative friction in finite time adiabatic processes) Carnot-like heat engines operate in finite time under the power law dissipation regime. We find that…

Statistical Mechanics · Physics 2020-04-22 M. Ponmurugan

The condition for stationary engines to attain the Carnot efficiency in and beyond the linear response regime is investigated. We find that this condition for finite-size engines is significantly different from that for macroscopic engines…

Statistical Mechanics · Physics 2017-05-23 Naoto Shiraishi

Classical thermodynamics aimed to quantify the efficiency of thermodynamic engines by bounding the maximal amount of mechanical energy produced compared to the amount of heat required. While this was accomplished early on, by Carnot and…

Optimization and Control · Mathematics 2020-01-22 Rui Fu , Amirhossein Taghvaei , Yongxin Chen , Tryphon T. Georgiou

The efficiency of an heat engine is traditionally defined as the ratio of its average output work over its average input heat. Its highest possible value was discovered by Carnot in 1824 and is a cornerstone concept in thermodynamics. It…

Statistical Mechanics · Physics 2015-06-19 Gatien Verley , Tim Willaert , Christian Van den Broeck , Massimiliano Esposito

We investigate the efficiency of a quantum Carnot engine based on open quantum dynamics theory. The model includes time-dependent external fields for the subsystems controlling the isothermal and isentropic processes and for the…

Statistical Mechanics · Physics 2022-08-24 Shoki Koyanagi , Yoshitaka Tanimura

Continuous particle exchange thermal machines require no time-dependent driving, can be realised in solid-state electronic devices, and miniaturised to nanometre scale. Quantum dots, providing a narrow energy filter and allowing to…

Mesoscale and Nanoscale Physics · Physics 2025-12-18 Eugenia Pyurbeeva , Ronnie Kosloff

Combining two disparate lines of thought like thermodynamics and quantum mechanics yields surprising results. The resulting idea of quantum thermodynamic engines holds promise for harvesting novel sources of energy of purely quantum origin,…

Quantum Physics · Physics 2025-04-30 H S Mani , N Ramadas , V V Sreedhar

We determine the statistics of work in isothermal volume changes of a classical ideal gas consisting of a single particle. Combining our results with the findings of Lua and Grosberg [J. Chem. Phys. B 109, 6805 (2005)] on adiabatic…

Statistical Mechanics · Physics 2015-06-15 Johannes Hoppenau , Markus Niemann , Andreas Engel

[...] By the beginning of the 20th century, the principles of thermodynamics were summarized into the so-called four laws, which were, as it turns out, definitive negative answers to the doomed quests for perpetual motion machines. As a…

History and Philosophy of Physics · Physics 2015-07-14 Henni Ouerdane , Yann Apertet , Christophe Goupil , Philippe Lecoeur

This work obtains the efficiency at maximum power for a stochastic heat engine performing Carnot-like, Stirling-like and Ericsson-like cycles. For the mesoscopic engine a Brownian particle trapped by an optical tweezers is considered. The…

Statistical Mechanics · Physics 2023-08-02 O. Contreras-Vergara , N. Sánchez-Salas , G. Valencia-Ortega , J. I. Jiménez-Aquino