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We identify a velocity distribution function of ideal gas particles that is compatible with the local equilibrium assumption and the fundamental thermodynamic relation satisfying the endoreversibility. We find that this distribution is a…

Statistical Mechanics · Physics 2017-07-19 Yuki Izumida , Koji Okuda

We study the efficiency at maximum power, $\eta^*$, of engines performing finite-time Carnot cycles between a hot and a cold reservoir at temperatures $T_h$ and $T_c$, respectively. For engines reaching Carnot efficiency $\eta_C=1-T_c/T_h$…

Statistical Mechanics · Physics 2015-05-19 Massimiliano Esposito , Ryoichi Kawai , Katja Lindenberg , Christian Van den Broeck

We study a molecular engine constituted by a gas of $N \sim 10^2$ molecules enclosed between a massive piston and a thermostat. The force acting on the piston and the temperature of the thermostat are cyclically changed with a finite period…

Statistical Mechanics · Physics 2015-03-19 Luca Cerino , Andrea Puglisi , Angelo Vulpiani

We analytically derive maximum efficiency at given cooling power for Carnot-type low-dissipation refrigerators. The corresponding optimal cycle duration depends on a single parameter, which is a specific combination of irreversibility…

Statistical Mechanics · Physics 2020-05-27 Viktor Holubec , Zhuolin Ye

Active matter constantly dissipates energy to power the self-propulsion of its microscopic constituents. This opens the door to designing innovative cyclic engines without any equilibrium equivalent. We offer a consistent thermodynamic…

Soft Condensed Matter · Physics 2020-07-08 Timothy Ekeh , Michael E. Cates , Étienne Fodor

We consider the optimization of a finite-time Carnot engine characterized by small dissipations. We bound the power with a simple inequality and show that the optimal strategy is to perform small cycles around a given working point, which…

Quantum Physics · Physics 2020-03-23 Paolo Abiuso , Martí Perarnau-Llobet

Originally, the Carnot cycle is a theoretical thermodynamic cycle that provides an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a…

General Finance · Quantitative Finance 2018-12-20 Constantin Udriste , Vladimir Golubyatnikov , Ionel Tevy

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

A long standing open problem whether a heat engine with finite power achieves the Carnot efficiency is investigated. We rigorously prove a general trade-off inequality on thermodynamic efficiency and time interval of a cyclic process with…

Statistical Mechanics · Physics 2017-08-18 Naoto Shiraishi , Hiroyasu Tajima

We consider an isothermal machine composed of two Brownian particles (say particle A and B) connected by a harmonic spring. A constant load is attached to particle A, and the particle B is trapped in a harmonic confinement whose minimum is…

Statistical Mechanics · Physics 2018-08-01 Deepak Gupta

We study universal aspects of fluctuations in an ensemble of noninteracting continuous quantum thermal machines in the steady state limit. Considering an individual machine, such as a refrigerator, in which relative fluctuations (and high…

Statistical Mechanics · Physics 2022-03-02 Matthew Gerry , Na'im Kalantar , Dvira Segal

Power and efficiency are fundamental criteria for evaluating the performance of thermodynamic cycles. However, it is generally impossible to maximize both simultaneously. In particular, achieving maximum efficiency inevitably leads to…

Statistical Mechanics · Physics 2026-01-28 R. X. Zhai , Xin Yue , C. P. Sun

We study temperature fluctuations in mesoscopic $N$-body systems undergoing non-equilibrium processes from the perspective of stochastic thermodynamics. By introducing a stochastic differential equation, we describe the evolution of the…

Statistical Mechanics · Physics 2026-05-19 Zhaoyu Fei , Yu-Han Ma

A dynamical model of a highly efficient heat engine is proposed, where an applied temperature difference maintains the motion of particles around the circuit consisting of two asymmetric narrow channels, in one of which the current flows…

Statistical Mechanics · Physics 2022-10-06 Giuliano Benenti , Giulio Casati , Fabio Marchesoni , Jiao Wang

Considering ideal paramagnetic medium, in this paper we deduced an expression for the thermal efficiency of Carnot heat engine with a paramagnetic gas as working substance. We found that the efficiency depends on the limits of maximum and…

Statistical Mechanics · Physics 2019-05-17 Manuel Malaver

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

At the very foundation of the second law of thermodynamics lies the fact that no heat engine operating between two reservoires of temperatures $T_C\leq T_H$ can overperform the ideal Carnot engine: $\langle W \rangle / \langle Q_H \rangle…

Statistical Mechanics · Physics 2014-06-18 Michele Campisi

When engineering microscopic machines, increasing efficiency can often come at a price of reduced reliability due to the impact of stochastic fluctuations. Here we develop a general method for performing multi-objective optimisation of…

Quantum Physics · Physics 2021-01-04 Harry J. D. Miller , Mohammad Mehboudi

A new universality in optimization of trade-off between power and efficiency for low-dissipation Carnot cycles is presented. It is shown that any trade-off measure expressible in terms of efficiency and the ratio of power to its maximum…

Statistical Mechanics · Physics 2016-05-05 Viktor Holubec , Artem Ryabov

For Markov processes over discrete configurations, an asymptotic bound on the uncertainty of stochastic fluxes is derived in terms of the harmonic mean of decay rates with respect to the stationary distribution. This bound is necessarily…

Statistical Mechanics · Physics 2024-07-16 Katarzyna Macieszczak