Searcharxiv⌕ Search

arXiv subjects

Ramandeep S. Johal

Publications and source records attributed to Ramandeep S. Johal.

At least 37 records · Page 2Linked to original sources
arXiv2020

Generalized golden mean and the efficiency of thermal machines

We investigate generic heat engines and refrigerators operating between two heat reservoirs, for the condition when their efficiencies are equal to each other. It is shown that the corresponding value of efficiency is given as the inverse of the generalized golden mean, $ϕ_p$, where the parameter $p$ depends on the degree of irreversibility of both engine and refrigerator. The reversible case ($p=1$) yields the efficiency in terms of the standard golden mean. We also extend the analysis to a three-heat-resrervoir setup.

physics.class-ph↗
arXiv2019

Performance optimization of low-dissipation thermal machines revisited

We revisit the optimization of performance of finite-time Carnot machines satisfying the low-dissipation assumption. The standard procedure seeks to optimize an objective function, such as power output of the engine, over the durations of contacts between the working medium and the heat reservoirs. This procedure may lead to unwieldy equations at the optimum of some objective functions. We propose an alternate scheme in which the output or input work is first optimized for a given cycle time, followed by an optimization of another objective function over the cycle time. The optimal behavior is thus obtained in a much simplified manner, with closed-form expressions for figures of merit. The approach is demonstrated for various objective functions, both for engines as well as refrigerators.

cond-mat.stat-mech↗
arXiv2019

Optimal Performance of a Three-level Quantum Refrigerator

We study the optimal performance of a three-level quantum refrigerator using two different objective functions: cooling power and $χ$-function. For both cases, we obtain general expressions for the coefficient of performance (COP) and derive its well-known lower and upper bounds for the limiting cases when the ratio of system-bath coupling constants at the hot and cold contacts approaches infinity and zero, respectively. We also show that the cooling power is optimizable only in the local region with respect to one control frequency, while $χ$-function can be optimized globally with respect to two control frequencies. Additionally, we show that in the low-temperatures regime, our model of refrigerator can be mapped to Feynman's ratchet and pawl model, a classical mesoscopic heat engine. In the parameter regime where both cooling power and $χ$-function can be optimized, we compare the cooling power of the quantum refrigerator at maximum $χ$-function with the optimum cooling power.

cond-mat.stat-mech↗
arXiv2019

Efficiency of a two-stage heat engine at optimal power

We propose a two-stage cycle for an optimized linear-irreversible heat engine that operates, in a finite time, between a hot (cold) reservoir and a finite auxiliary system acting as a sink (source) in the first (second) stage. Under the tight-coupling condition, the engine shows the low-dissipation behavior in each stage, i.e. the entropy generated depends inversely on the duration of the process. The phenomenological dissipation constants are determined within the theory itself in terms of the heat transfer coefficients and the heat capacity of the auxiliary system. We study the efficiency at maximum power and highlight a class of efficiencies in the symmetric case that show universality up to second order in Carnot efficiency, while Curzon-Ahlborn efficiency is obtained as the lower bound for this class.

cond-mat.stat-mech↗
arXiv2019

The many avatars of Curzon-Ahlborn efficiency

Efficiency at maximum power output of irreversible heat engines has attracted a lot of interest in recent years. We discuss the occurance of a particularly simple and elegant formula for this efficiency in various different models. The so-called Curzon-Ahlborn efficiency is given by the square-root formula: $1-\sqrt{T_c/T_h}$, where $T_c$ and $T_h$ are the cold and hot reservoir temperatures.

cond-mat.stat-mech↗
arXiv2019

Three-level laser heat engine at optimal performance with ecological function

Although classical and quantum heat engines work on entirely different fundamental principles, there is an underlying similarity. For instance, the form of efficiency at optimal performance may be similar for both types of engines. In this work, we study a three-level laser quantum heat engine operating at maximum ecological function (EF) which represents a compromise between the power output and the loss of power due to entropy production. We derive analytic expressions for efficiency under the assumptions of strong matter-field coupling and high bath temperatures. Upper and lower bounds on the efficiency exist in case of extreme asymmetric dissipation when the ratio of system-bath coupling constants at the hot and the cold contacts respectively approaches, zero or infinity. These bounds have been established previously for various classical models of Carnot-like engines. We conclude that while the engine produces at least 75\% of the power output as compared with the maximum power conditions, the fractional loss of power is appreciably low in case of the engine operating at maximum EF, thus making this objective function relevant from an environmental point of view.

quant-ph↗
arXiv2018

Thermoelectric generator at optimal power with external and internal irreversibilities

There are few exact results on optimal power conditions for a thermoelectric generator in the presence of both external and internal irreversibilities---modelled as non-ideal thermal contacts and Joule heating, respectively. Simplified cases, where only one kind of irreversibility is assumed, yield some well-known expressions for efficiency at maximum power (EMP), such as Curzon-Ahlborn efficiency for endoreversible model. In this work, we analyze situations under the simultaneous presence of internal and external irreversibilities. To simplify, we neglect heat leaks, and each kind of irreversibility is assumed only on the side of one of the thermal contacts. We also present the symmetric case---where each kind of irreversibility contributes with equal strengths towards the side of each thermal contact. We show the bounds satisfied by EMP in each of these regimes and compare its properties for thermal impedence matching and close to equilibrium, where we find step-wise changes in EMP.

cond-mat.stat-mech↗
arXiv2018

Low-dissipation Carnot-like heat engines at maximum efficient power

We study the optimal performance of Carnot-like heat engines working in low dissipation regime using the product of the efficiency and the power output, also known as the efficient power, as our objective function. Efficient power function represents the best trade-off between power and efficiency of a heat engine. We find lower and upper bounds on the efficiency in case of extreme asymmetric dissipation when the ratio of dissipation coefficients at the cold and the hot contacts approaches, respectively, zero or infinity. In addition, we obtain the form of efficiency for the case of symmetric dissipation. We also discuss the universal features of efficiency at maximum efficient power and derive the bounds on the efficiency using global linear-irreversible framework introduced recently by one of the authors.

cond-mat.stat-mech↗
arXiv2018

Feynman-Smoluchowski engine at high temperatures and the role of constraints

Feynman's ratchet and pawl is a paradigmatic model for energy conversion using thermal fluctuations in the mesoscopic regime. Here, we optimize the power output of the ratchet as a heat engine in the high temperatures limit, and derive the universality of efficiency at maximum power up to second order, using a non-linear approximation. On the other hand, the linear model may be optimized by constraining the internal energy scales in different ways. It is shown that simple constraints lead to well-known expressions of thermal efficiency in finite-time thermodynamics. Thereby, the constrained ratchet, in the linear regime, has been mapped to an effective finite-time thermodynamic model.

cond-mat.stat-mech↗
arXiv2018

Global linear-irreversible principle for optimization in finite-time thermodynamics

There is intense effort into understanding the universal properties of finite-time models of thermal machines---at optimal performance---such as efficiency at maximum power, coefficient of performance at maximum cooling power, and other such criteria. In this letter, a {\it global} principle consistent with linear irreversible thermodynamics is proposed for the whole cycle---without considering details of irreversibilities in the individual steps of the cycle. This helps to express the total duration of the cycle as $τ\propto {\bar{Q}^2}/{Δ_{\rm tot} S}$, where $\bar{Q}$ models the effective heat transferred through the machine during the cycle, and $Δ_{\rm tot} S$ is the total entropy generated. By taking $\bar{Q}$ in the form of simple algebraic means (such as arithmetic and geometric means) over the heats exchanged by the reservoirs, the present approach is able to predict various standard expressions for figures of merit at optimal performance, as well as the bounds respected by them. It simplifies the optimization procedure to a one-parameter optimization, and provides a fresh perspective on the issue of universality at optimal performance, for small difference in reservoir temperatures. As an illustration, we compare performance of a partially optimized four-step endoreversible cycle with the present approach.

cond-mat.stat-mech↗
arXiv2017

Quantum Otto engine with exchange coupling in the presence of level degeneracy

We consider a quasi-static quantum Otto cycle using two effectively two-level systems with degeneracy in the excited state. The systems are coupled through isotropic exchange interaction of strength $J>0$, in the presence of an external magnetic field $B$ which is varied during the cycle. We prove the positive work condition, and show that level-degeneracy can act as a thermodynamic resource, so that a larger amount of work can be extracted than from the non-degenerate case, both with and without coupling. We also derive an upper bound for the efficiency of the cycle. This bound is the same as derived for a system of coupled spin-1/2 particles [G. Thomas and R. S. Johal, Phys. Rev. E {\bf 83}, 031135 (2011)] i.e. without degeneracy, and depends only on the control parameters of the Hamiltonian, but is independent of the level degeneracy and the reservoir temperatures.

cond-mat.stat-mech↗
arXiv2017

Heat engines at optimal power: Low-dissipation versus endoreversible model

Low-dissipation model and the endoreversible model of heat engines are two of the most commonly studied models of machines in finite-time thermodynamics. In this paper, we compare the performance characteristics of these two models under optimal power output. We point out a basic equivalence between them, in the linear response regime.

cond-mat.stat-mech↗
arXiv2016

Optimal performance of heat engines with a finite source or sink and inequalities between means

Given a system with a finite heat capacity and a heat reservoir, and two values of initial temperatures, $T_+$ and $T_- (< T_+)$, we enquire, in which case the optimal work extraction is larger: when the reservoir is an infinite source at $T_+$ and the system is a sink at $T_-$, or, when the reservoir is an infinite sink at $T_-$ and the system acts as a source at $T_+$? It is found that in order to compare the total extracted work, and the corresponding efficiency in the two cases, we need to consider three regimes as suggested by an inequality, the so-called arithmetic mean-geometric mean inequality, involving the arithmetic and the geometric means of the two temperature values $T_+$ and $T_-$. In each of these regimes, the efficiency at total work obeys certain universal bounds, given only in terms of the ratio of initial temperatures. The general theoretical results are exemplified for thermodynamic systems for which internal energy and temperature are power laws of the entropy. The conclusions may serve as benchmarks in the design of heat engines, where we can choose the nature of the finite system, so as to tune the total extractable work and/or the corresponding efficiency.

cond-mat.stat-mech↗
arXiv2016

Efficiencies of power plants, quasi-static models and the geometric-mean temperature

Observed efficiencies of industrial power plants are often approximated by the square-root formula: $1-\sqrt{T_-/T_+}$, where $T_+ (T_-)$ is the highest (lowest) temperature achieved in the plant. This expression can be derived within finite-time thermodynamics, or, by entropy generation minimization, based on finite rates of processes. A closely related quantity is the optimal value of the intermediate temperature for the hot stream, which is given by the geometric-mean value: $\sqrt{T_+ T_-}$. It is proposed to model the operation of plants by quasi-static work extraction models, with one reservoir (source/sink) as finite, while the other as practically infinite. No simplifying assumption is made on the nature of the finite system. This description is consistent with two model hypotheses, each yielding a specific value of the intermediate temperature. We show that the expected value of the intermediate temperature, defined as the arithmetic mean, is very closely given by the geometric-mean value. The definition is motivated as the use of inductive inference in the presence of limited information.

cond-mat.stat-mech↗
arXiv2015

Near-equilibrium universality and bounds on efficiency in quasi-static regime with finite source and sink

We show the validity of some results of finite-time thermodynamics, also within the quasi-static framework of classical thermodynamics. First, we consider the efficiency at maximum work (EMW) from finite source and sink modelled as identical thermodynamic systems. The near-equilibrium regime is characterized by expanding the internal energy upto second order (i.e. upto linear response) in the difference of initial entropies of the source and the sink. It is shown that the efficiency is given by a universal expression $2 η_C / (4-η_C)$, where $η_C$ is the Carnot efficiency. Then, different sizes of source and sink are treated, by combining different numbers of copies of the same thermodynamic system. The efficiency of this process is found to be ${\boldsymbolη}_0 = η_C/ (2-γη_C)$, where the parameter $γ$ depends only on the relative size of the source and the sink. This implies that within the linear response theory, EMW is bounded as ${η_C}/{2} \le {\boldsymbolη}_0 \le {η_C}/{(2 - η_C)}$, where the upper (lower) bound is obtained with a sink much larger (smaller) in size than the source. We also remark on the behavior of the efficiency beyond linear response.

cond-mat.stat-mech↗
arXiv2015

Estimating performance of Feynman's ratchet with limited information

We estimate the performance of Feynman's ratchet at given values of the ratio of cold to hot reservoir temperatures ($θ$) and the figure of merit (efficiency in the case of engine and coefficienct of performance in the case of refrigerator). The latter implies that only the ratio of two intrinsic energy scales is known to the observer, but their exact values are completely uncertain. The prior probability distribution for the uncertain energy parameters is argued to be Jeffreys' prior. We define an average measure for performance of the model by averaging, over the prior distribution, the power output (heat engine) or the $χ$-criterion (refrigerator) which is the product of rate of heat absorbed from the cold reservoir and the coefficient of performance. We observe that the figure of merit, at optimal performance close to equilibrium, is reproduced by the prior-averaging procedure. Further, we obtain the well-known expressions of finite-time thermodynamics for the efficiency at optimal power and the coefficient of performance at optimal $χ$-criterion, given by $1-\sqrtθ$ and $1/\sqrt{1-θ}-1$ respectively. This analogy is explored further and we point out that the expected heat flow from and to the reservoirs, behaves as an effective Newtonian flow. We also show, in a class of quasi-static models of quantum heat engines, how CA efficiency emerges in asymptotic limit with the use of Jeffreys' prior.

cond-mat.stat-mech↗
arXiv2015

Optimal engine performance using inference for non-identical finite source and sink

We quantify the prior information to infer the optimal characteristics for a constrained thermodynamic process of maximum work extraction for a pair of non-identical finite systems. The total entropy of the whole system remains conserved. The ignorance is assumed about the final temperature of the finite systems and then a prior distribution is assigned to the unknown temperatures. We derive the estimates of efficiency for this reversible model of heat engine with incomplete information. The estimates show good agreement with efficiency at optimal work for arbitrary sizes of systems, however the estimates become exact when one of the reservoir becomes very large in comparison to the other.

cond-mat.stat-mech↗