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Carnot efficiency sets a fundamental upper bound on the heat engine efficiency, attainable in the quasi-static limit, albeit at the cost of completely sacrificing power output. In this Letter, we present a minimal heat engine model that can…

Statistical Mechanics · Physics 2025-01-17 Shiling Liang , Yu-Han Ma , Daniel Maria Busiello , Paolo De Los Rios

The constraint relation for efficiency and power is crucial to design optimal heat engines operating within finite time. We find a universal constraint between efficiency and output power for heat engines operating in the low-dissipation…

Quantum Physics · Physics 2018-10-09 Yu-Han Ma , Dazhi Xu , Hui Dong , Chang-Pu Sun

We study a thermal engine model for which Newton's cooling law is obeyed during heat transfer processes. The thermal efficiency and its bounds at maximum output power are derived and discussed. This model, though quite simple, can be…

Statistical Mechanics · Physics 2012-11-30 H. Yan , Hao Guo

We present a new outlook on the climate system thermodynamics, studying some of its macroscopic properties in terms of the 1st and 2nd laws of thermodynamics. We review and clarify the notion of efficiency of the climate system by…

Atmospheric and Oceanic Physics · Physics 2011-10-11 Valerio Lucarini

The Carnot heat engine sets an upper bound on the efficiency of a heat engine. As an ideal, reversible engine, a single cycle must be performed in infinite time, and so the Carnot engine has zero power. However, there is nothing in…

High Energy Physics - Theory · Physics 2018-07-11 Clifford V. Johnson

The efficient conversion of thermal energy to mechanical work by a heat engine is an ongoing technological challenge. Since the pioneering work of Carnot, it is known that the efficiency of heat engines is bounded by a fundamental upper…

Mesoscale and Nanoscale Physics · Physics 2017-09-20 Jan Klaers , Stefan Faelt , Atac Imamoglu , Emre Togan

We formulate the work output and efficiency for linear irreversible heat engines working between a finite-sized hot heat source and an infinite-sized cold heat reservoir until the total system reaches the final thermal equilibrium state…

Statistical Mechanics · Physics 2015-06-17 Yuki Izumida , Koji Okuda

The Carnot cycle is a prototype of ideal heat engine to draw mechanical energy from the heat flux between two thermal baths with the maximum efficiency, dubbed as the Carnot efficiency $\eta_{\mathrm{C}}$. Such efficiency can only be…

Statistical Mechanics · Physics 2022-06-22 Ruo-Xun Zhai , Fang-Ming Cui , Yu-Han Ma , C. P. Sun , Hui Dong

We consider the efficiency of turbulence, a dimensionless parameter that characterises the fraction of the input energy stored into a turbulent flow field. We first show that the inverse of the efficiency provides an upper bound for the…

Fluid Dynamics · Physics 2025-08-11 A Lopez , A Barral , G Costa , Q Pikeroen , V Shukla , Bérengère Dubrulle

We consider a rudimentary model for a heat engine, known as the Brownian gyrator, that consists of an overdamped system with two degrees of freedom in an anisotropic temperature field. Whereas the hallmark of the gyrator is a nonequilibrium…

Statistical Mechanics · Physics 2021-10-13 Olga Movilla Miangolarra , Amirhossein Taghvaei , Rui Fu , Yongxin Chen , Tryphon T. Georgiou

We investigate fluctuations of output work for a class of Stirling heat engines with working fluid composed of interacting units and compare these fluctuations to an average work output. In particular, we focus on engine performance close…

Statistical Mechanics · Physics 2017-09-08 Viktor Holubec , Artem Ryabov

Evaluating the maximum amount of work extractable from a nanoscale quantum system is one of the central problems in quantum thermodynamics. Previous works identified the free energy of the input state as the optimal rate of extractable work…

Quantum Physics · Physics 2026-03-06 Kaito Watanabe , Ryuji Takagi

We propose a new form of the Second Law inequality that defines a tight bound for extractable work from the non-equilibrium quantum state. In classical thermodynamics, the optimal work is given by the difference of free energy, what…

Quantum Physics · Physics 2023-02-14 Marcin Łobejko

Heat is a physical manifestation of entropy, where the removal of entropy from a thermal energy reservoir permits the conversion of heat into work. This entropy transfer is facilitated by the cold thermal energy reservoir in typical heat…

Quantum Physics · Physics 2025-11-12 Liam Judd McClelland

Betz's law, purportedly, says an ideal wind harvester cannot extract more than 16/27 ($\sim$59\%) of the wind energy. As the law's derivation relies on momentum and energy conservation with incompressible flow and not the physical mechanism…

Fluid Dynamics · Physics 2023-02-21 Charlie E. M. Strauss

Heat engines extract work by running cyclically between two heat reservoirs. When the two reservoirs are thermal and at different temperatures, the maximum efficiency of the engine is given by the Carnot limit. Here we consider a quantum…

Quantum Physics · Physics 2014-02-03 Johannes Roßnagel , Obinna Abah , Ferdinand Schmidt-Kaler , Kilian Singer , Eric Lutz

We study a class of cyclic Brownian heat engines in the framework of finite-time thermodynamics. For infinitely long cycle times, the engine works at the Carnot efficiency limit producing, however, zero power. For the efficiency at maximum…

Statistical Mechanics · Physics 2009-11-13 Tim Schmiedl , Udo Seifert

The work content of non-equilibrium systems in relation to a heat bath is often analyzed in terms of expectation values of an underlying random work variable. However, we show that when optimizing the expectation value of the extracted…

Quantum Physics · Physics 2015-03-19 Johan Aberg

In many real-world situations, there are constraints on the ways in which a physical system can be manipulated. We investigate the entropy production (EP) and extractable work involved in bringing a system from some initial distribution $p$…

Statistical Mechanics · Physics 2022-11-22 Artemy Kolchinsky , David H. Wolpert

We present quantitative relations between work and information that are valid both for finite sized and internally correlated systems as well in the thermodynamical limit. We suggest work extraction should be viewed as a game where the…

Quantum Physics · Physics 2015-05-13 Oscar C. O. Dahlsten , Renato Renner , Elisabeth Rieper , Vlatko Vedral