scholarly journals Bound on Efficiency of Heat Engine from Uncertainty Relation Viewpoint

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 439
Author(s):  
Pritam Chattopadhyay ◽  
Ayan Mitra ◽  
Goutam Paul ◽  
Vasilios Zarikas
Keyword(s):  
Uncertainty Relation ◽  
Heat Engine ◽  
Upper And Lower Bounds ◽  
Engine Model ◽  
Heat Engines ◽  
Quantum Heat Engine ◽  
Quantum Observables ◽  
Thermodynamic Variables ◽  
Work Done ◽  
The Relationship

Quantum cycles in established heat engines can be modeled with various quantum systems as working substances. For example, a heat engine can be modeled with an infinite potential well as the working substance to determine the efficiency and work done. However, in this method, the relationship between the quantum observables and the physically measurable parameters—i.e., the efficiency and work done—is not well understood from the quantum mechanics approach. A detailed analysis is needed to link the thermodynamic variables (on which the efficiency and work done depends) with the uncertainty principle for better understanding. Here, we present the connection of the sum uncertainty relation of position and momentum operators with thermodynamic variables in the quantum heat engine model. We are able to determine the upper and lower bounds on the efficiency of the heat engine through the uncertainty relation.

scholarly journals Bound on Efficiency of Heat Engine From Uncertainty Relation Viewpoint

2021 ◽  
Author(s):  
Ayan Mitra ◽  
Pritam Chattapadhyay ◽  
Goutam Paul ◽  
Vasilios Zarikas
Keyword(s):  
Uncertainty Relation ◽  
Heat Engine ◽  
Upper And Lower Bounds ◽  
Engine Model ◽  
Heat Engines ◽  
Quantum Heat Engine ◽  
Quantum Observables ◽  
Thermodynamic Variables ◽  
Work Done ◽  
The Relationship

Abstract Quantum cycles in established heat engines can be modeled with various quantum systems as working substances. As for example, heat engine can be modeled with an infinite potential well as the working substance to determine the efficiency and work done. However, in this method, the relationship between the quantum observables and the physically measurable parameters, i.e., the efficiency and work done is not well understood from the quantum mechanics approach. A detailed analysis is needed to link the thermodynamical variables (on which the efficiency and work done depends) with the uncertainty principle for better understanding. Here, we present the connection of sum uncertainty relation of position and momentum operators with thermodynamic variables in the quantum heat engine model. We are able to determine the upper and lower bounds on the efficiency of the heat engine through uncertainty relation.

scholarly journals Relativistic quantum heat engine from uncertainty relation standpoint

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Pritam Chattopadhyay ◽  
Goutam Paul
Keyword(s):  
Uncertainty Relation ◽  
Relativistic Quantum ◽  
Heat Engine ◽  
Potential Well ◽  
Relativistic Case ◽  
Heat Engines ◽  
Quantum Heat Engine ◽  
Thermodynamic Variables ◽  
The One ◽  
Work Done

AbstractEstablished heat engines in quantum regime can be modeled with various quantum systems as working substances. For example, in the non-relativistic case, we can model the heat engine using infinite potential well as a working substance to evaluate the efficiency and work done of the engine. Here, we propose quantum heat engine with a relativistic particle confined in the one-dimensional potential well as working substance. The cycle comprises of two isothermal processes and two potential well processes of equal width, which forms the quantum counterpart of the known isochoric process in classical nature. For a concrete interpretation about the relation between the quantum observables with the physically measurable parameters (like the efficiency and work done), we develop a link between the thermodynamic variables and the uncertainty relation. We have used this model to explore the work extraction and the efficiency of the heat engine for a relativistic case from the standpoint of uncertainty relation, where the incompatible observables are the position and the momentum operators. We are able to determine the bounds (the upper and the lower bounds) of the efficiency of the heat engine through the thermal uncertainty relation.

scholarly journals Entropy Exchange and Thermodynamic Properties of the Single Ion Cooling Process

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 650
Author(s):  
Jian-Guo Miao ◽  
Chun-Wang Wu ◽  
Wei Wu ◽  
Ping-Xing Chen
Keyword(s):  
Thermodynamic Properties ◽  
Heat Engine ◽  
Entropy Change ◽  
Quantum Thermodynamics ◽  
Cooling Process ◽  
Cooling Cycle ◽  
Heat Engines ◽  
Quantum Heat Engine ◽  
Ion Cooling ◽  
Complete Quantum

A complete quantum cooling cycle may be a useful platform for studying quantum thermodynamics just as the quantum heat engine does. Entropy change is an important feature which can help us to investigate the thermodynamic properties of the single ion cooling process. Here, we analyze the entropy change of the ion and laser field in the single ion cooling cycle by generalizing the idea in Reference (Phys. Rev. Lett. 2015, 114, 043002) to a single ion system. Thermodynamic properties of the single ion cooling process are discussed and it is shown that the Second and Third Laws of Thermodynamics are still strictly held in the quantum cooling process. Our results suggest that quantum cooling cycles are also candidates for the investigation on quantum thermodynamics besides quantum heat engines.

A Novel Approach to the Teaching of Etropy Based on a Recent Single Particle Heat Engine Model

2006 ◽  
Author(s):  
W. John Dartnall ◽  
John Reizes
Keyword(s):  
Single Particle ◽  
Heat Engine ◽  
Working Fluid ◽  
Second Law ◽  
Piston Engine ◽  
New Approach ◽  
Engine Model ◽  
Mechanics Model ◽  
Heat Engines ◽  
Novel Approach

In a recently developed simple particle mechanics model in which a single particle represents the working fluid (gas) in a heat engine (exemplified by a piston engine) a new approach was outlined for the teaching of concepts to thermodynamic students. By mechanics reasoning a model was developed that demonstrates the connection between the Carnot efficiency limitation of heat engines and the Kelvin-Planck statement of Second Law requiring only the truth of the Clausius statement. In this paper the model is extended to introduce entropy. Here the particle's entropy is defined as a function of its kinetic energy and the space that it occupies that is analogous to that normally found in classical macroscopic analyses.

scholarly journals Optimization, Stability, and Entropy in Endoreversible Heat Engines

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1323
Author(s):  
Julian Gonzalez-Ayala ◽  
José Miguel Mateos Roco ◽  
Alejandro Medina ◽  
Antonio Calvo Hernández
Keyword(s):  
Heat Transfer ◽  
Stationary State ◽  
Entropy Generation ◽  
Pareto Front ◽  
Heat Engine ◽  
Heat Fluxes ◽  
Working Fluid ◽  
Input Output ◽  
Engine Model ◽  
Heat Engines

The stability of endoreversible heat engines has been extensively studied in the literature. In this paper, an alternative dynamic equations system was obtained by using restitution forces that bring the system back to the stationary state. The departing point is the assumption that the system has a stationary fixed point, along with a Taylor expansion in the first order of the input/output heat fluxes, without further specifications regarding the properties of the working fluid or the heat device specifications. Specific cases of the Newton and the phenomenological heat transfer laws in a Carnot-like heat engine model were analyzed. It was shown that the evolution of the trajectories toward the stationary state have relevant consequences on the performance of the system. A major role was played by the symmetries/asymmetries of the conductance ratio σhc of the heat transfer law associated with the input/output heat exchanges. Accordingly, three main behaviors were observed: (1) For small σhc values, the thermodynamic trajectories evolved near the endoreversible limit, improving the efficiency and power output values with a decrease in entropy generation; (2) for large σhc values, the thermodynamic trajectories evolved either near the Pareto front or near the endoreversible limit, and in both cases, they improved the efficiency and power values with a decrease in entropy generation; (3) for the symmetric case (σhc=1), the trajectories evolved either with increasing entropy generation tending toward the Pareto front or with a decrease in entropy generation tending toward the endoreversible limit. Moreover, it was shown that the total entropy generation can define a time scale for both the operation cycle time and the relaxation characteristic time.

scholarly journals Space-fractional quantum heat engine based on level degeneracy

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ekrem Aydiner
Keyword(s):  
Heat Engine ◽  
Tuning Parameter ◽  
Potential Well ◽  
Fractional Quantum ◽  
Heat Engines ◽  
Quantum Heat Engine ◽  
Large Size ◽  
Level Degeneracy ◽  
Infinite Potential Well ◽  
Quantum Heat Engines

AbstractIn order to examine the work and efficiency of the space-fractional quantum heat engine, we consider a model of the space-fractional quantum heat engine which has a Stirling-like cycle with a single particle under infinite potential well as an example. We numerically compute the work and efficiency for various fractional exponents. We show the work and the efficiency of the engine depending on the length of the potential well and fractional exponent of the engine. Furthermore, we show that fractional exponent plays a substantial role in the operating range of the quantum heat engine. Thus, we conclude that the fractional parameter can be used as a tuning parameter to obtain positive work and efficiency for the large size of the quantum heat engine. Additionally, the numerical results and model imply that the size of the engine can be enlarged in the nano-scale by using fractional deformations. As a result, in this study, we have not only shown that fractional deformations in space play an important role on the work and efficiency of the quantum heat engines but also introduced the concept of fractional quantum heat engines to the literature.

Quantum Optomechanics Thermodynamics and Heat Engines

2020 ◽  
pp. 399-450
Author(s):  
Pierre Meystre
Keyword(s):  
Thermal Noise ◽  
Heat Engine ◽  
Experimental Tests ◽  
Heat Pumps ◽  
Quantum Mechanical ◽  
Quantum Thermodynamics ◽  
Heat Engines ◽  
Quantum Heat Engine ◽  
Quantum Optomechanics ◽  
Thermodynamic Processes

This chapter addresses topics in quantum thermodynamics, where optomechanics may contribute attractive experimental tests and additional understanding. Quantum thermodynamics can be defined as the study of thermodynamics when quantum mechanical noise coexists with thermal noise and has a significant impact on the dynamics. This chapter focuses on the example of an optomechanical quantum heat engine (QHE). Section 11.2 reviews some questions about quantum work. Section 11.3 then outlines the steps leading to the formulation of continuous measurements in terms of stochastic Schrödinger equations. Section 11.4 reviews the main characteristics of QHE, comparing thermodynamic processes and engine cycles in the classical and quantum regimes. The opportunities offered by quasiparticles in the operation of QHE justify reviewing their properties in some detail (section 11.5), before introducing the optomechanical QHE system (section 11.6). Section 11.7 discusses the properties of the engine, and section 11.8 expands the discussion to polariton based quantum heat pumps.

scholarly journals Measurement Based Quantum Heat Engine with Coupled Working Medium

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1131 ◽  
Author(s):  
Arpan Das ◽  
Sibasish Ghosh
Keyword(s):  
Heat Engine ◽  
Coupling Constants ◽  
Cyclic Process ◽  
Coupling Constant ◽  
Quantum Heat Engine ◽  
Working Medium ◽  
Single Temperature ◽  
Higher Spin ◽  
Higher Spins ◽  
The Relationship

We consider measurement based single temperature quantum heat engine without feedback control, introduced recently by Yi, Talkner and Kim [Phys. Rev. E 96, 022108 (2017)]. Taking the working medium of the engine to be a one-dimensional Heisenberg model of two spins, we calculate the efficiency of the engine undergoing a cyclic process. Starting with two spin-1/2 particles, we investigate the scenario of higher spins also. We show that, for this model of coupled working medium, efficiency can be higher than that of an uncoupled one. However, the relationship between the coupling constant and the efficiency of the engine is rather involved. We find that in the higher spin scenario efficiency can sometimes be negative (this means work has to be done to run the engine cycle) for certain range of coupling constants, in contrast to the aforesaid work of Yi, Talkner and Kim, where they showed that the extracted work is always positive in the absence of coupling. We provide arguments for this negative efficiency in higher spin scenarios. Interestingly, this happens only in the asymmetric scenarios, where the two spins are different. Given these facts, for judiciously chosen conditions, an engine with coupled working medium gives advantage for the efficiency over the uncoupled one.

The Second Law of Thermodynamics in a Quantum Heat Engine Model

2006 ◽  
Vol 45 (3) ◽  
pp. 417-420 ◽  
Author(s):  
Zhang Ting ◽  
Cai Li-Feng ◽  
Chen Ping-Xing ◽  
Li Cheng-Zu
Keyword(s):  
Heat Engine ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Engine Model ◽  
Quantum Heat Engine
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