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Asymmetric quantum harmonic Otto engine under hot squeezed thermal reservoir

  • Monika , Kirandeep Kaur ORCID logo , Varinder Singh and Shishram Rebari EMAIL logo
Published/Copyright: April 14, 2025
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Journal of Non-Equilibrium Thermodynamics
From the journal Journal of Non-Equilibrium Thermodynamics Volume 50 Issue 3

Abstract

We study a quantum harmonic Otto engine under a hot squeezed thermal reservoir with asymmetry between the two adiabatic branches introduced by considering different speeds of the driving protocols. In the first configuration, the driving protocol for the expansion stroke is sudden-switch in nature and compression stroke is driven adiabatically, while the second configuration deals with the converse situation. In both cases, we obtain analytic expressions for the upper bound on efficiency and efficiency at optimal work output, which reveals a significant difference between the two configurations. Additionally, we find that the maximum achievable efficiency in sudden expansion case is 1/2 only while it approaches unity for the sudden compression stroke. Further, we study the effect of increasing degree of squeezing on the efficiency and work output of the engine and indicate the optimal operational regime for both configurations under consideration. Finally, by studying the full phase-diagram of the Otto cycle we observe that the operational region of the engine mode grows with increasing squeezing at the expense of refrigeration regime.

Keywords: Otto engine; harmonic oscillator; squeezing; phase diagram
Corresponding author: Shishram Rebari, Department of Physics, Dr B R Ambedkar National Institute of Technology Jalandhar, Jalandhar, Punjab, 144008, India, E-mail: 

  1. Research ethics: The local Institutional Review Board deemed the study exempt from review.

  2. Informed consent: Not applicable.

  3. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: Authors state no conflict of interest.

  6. Research funding: Monika is thankful to the government of India for providing financial support for this work via an Institute fellowship under Dr. B. R. Ambedkar National Institute of Technology Jalandhar. V. S. acknowledges the financial support through the KIAS Individual Grant No. PG096801 at Korea Institute for Advanced Study.

  7. Data availability: Not applicable.

Appendix A: Casus irreducibilis

While solving the cubic equations, there may arise the case of casus irreducibis when the discriminant D = 18abcd − 4b 3 d + b 2 c 2 − 4ac 3 − 27a 2 d 2, of the cubic equation [42]

(A1) a y 3 + b y 2 + c y + d = 0 ,

is greater than 0, i. e. D > 0. The above equation can be expressed in the following form,

(A2) y 3 + A y 2 + B y + C = 0 ,

where A = b/a, B = c/a and C = d/a. The solution of the above equation can be obtained in terms of trigonometric functions and is given by

(A3) y = − A 3 + 2 3 A 2 − 3 B cos 1 3 cos − 1 − 2 A 3 − 9 A B + 27 C 2 ( A 2 − 3 B ) 3 / 2 .

We will obtain solution of cubic equations in this way for two cases which are discussed in the present paper.

A.1 Sudden expansion case

For the sudden expansion stroke, discriminant D of the equation,

(A4) z 3 − 3 z 2 ⁡ τ 2 ⁡ cosh ( 2 r ) + τ 2 τ − cosh ( 2 r ) 2 ⁡ cosh 2 ( 2 r ) = 0 ,

is given by D = 108 τ 2 2 τ − cosh ( 2 r ) τ − cosh ( 2 r ) 2 ⁡ cosh 3 ( 2 r ) > 0 . Here, A = −3τ/2cosh(2r), B = 0, C = τ 2 τ − cosh ( 2 r ) / 2 ⁡ cosh 2 ( 2 r ) .

A.2 Sudden compression case

In our case, the discriminant of cubic equation

(A5) z 3 − z 3 τ ⁡ cosh ( 2 r ) cosh ( 2 r ) 2 ⁡ cosh ( 2 r ) − τ + 2 τ 2 cosh ( 2 r ) 2 ⁡ cosh ( 2 r ) − τ = 0

will be D = 108 τ 3 2 ⁡ cosh ( 2 r ) − τ τ − cosh ( 2 r ) 2 ⁡ cosh 2 ( 2 r ) > 0. Here, A = 0, B = − 3 τ ⁡ cosh ( 2 r ) / cosh ( 2 r ) 2 ⁡ cosh ( 2 r ) − τ , C = 2 τ 2 / cosh ( 2 r ) 2 ⁡ cosh ( 2 r ) − τ .

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Received: 2024-11-27
Accepted: 2025-03-31
Published Online: 2025-04-14
Published in Print: 2025-07-28

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/jnet-2024-0110
Keywords for this article
Otto engine; harmonic oscillator; squeezing; phase diagram

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. Heat transfer at nano-scale and boundary conditions: a comparison between the Guyer-Krumhansl model and the Thermomass theory
  4. Exergy-based efficient ecological-function optimization for endoreversible Carnot refrigerators
  5. Effect of depositional nanoparticles on heat transfer at the solid–liquid interface using molecular dynamics simulations
  6. Optimization of injection parameters, and ethanol shares for cottonseed biodiesel fuel in diesel engine utilizing artificial neural network (ANN) and taguchi grey relation analysis (GRA)
  7. A general relativistic kinetic theory approach to linear transport in generic hydrodynamic frame
  8. Asymmetric quantum harmonic Otto engine under hot squeezed thermal reservoir
  9. Approaches of finite-time thermodynamics in conceptual design of heat exchange systems
  10. Thermal transport in a silicon/diamond micro-flake with quantum dots inserts
  11. Finite element analysis on generalized piezothermoelastic interactions in an unbounded piezoelectric medium containing a spherical cavity
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