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Ramandeep S. Johal

Publications and source records attributed to Ramandeep S. Johal.

At least 55 records · Page 3Linked to original sources
arXiv2014

Efficiency at optimal work from finite reservoirs: a probabilistic perspective

We revisit the classic thermodynamic problem of maximum work extraction from two arbitrary sized hot and cold reservoirs, modelled as perfect gases. Assuming ignorance about the extent to which the process has advanced, which implies an ignorance about the final temperatures, we quantify the prior information about the process and assign a prior distribution to the unknown temperature(s). This requires that we also take into account the temperature values which are regarded to be unphysical in the standard theory, as they lead to a contradiction with the physical laws. Instead in our formulation, such values appear to be consistent with the given prior information and hence are included in the inference. We derive estimates of the efficiency at optimal work from the expected values of the final temperatures, and show that these values match with the exact expressions in the limit when any one of the reservoirs is very large compared to the other. For other relative sizes of the reservoirs, we suggest a weighting procedure over the estimates from two valid inference procedures, that generalizes the procedure suggested earlier in [J. Phys. A: Math. Theor. {\bf 46}, 365002 (2013)]. Thus a mean estimate for efficiency is obtained which agrees with the optimal performance to a high accuracy.

cond-mat.stat-mech↗
arXiv2014

On the form of prior for constrained thermodynamic processes with uncertainty

We consider the standard thermodynamic processes with constraints, but with additional uncertainty about the control parameters. Motivated by inductive reasoning, we assign prior distribution that provides a rational guess about likely values of the uncertain parameters.The priors are derived explicitly for both the entropy conserving and the energy conserving processes. The proposed form is useful when the constraint equation cannot be treated analytically. The inference is performed using spin-1/2 systems as models for heat reservoirs. Analytical results are derived in the high temperatures limit. Comparisons are found between the estimates of thermal quantities and the optimal values described by extremum principles. We also seek a intuitive interpretation of the prior and show that it becomes uniform over the quantity which is conserved in the process. We find further points of correspondence between the inference based approach and the thermodynamic framework.

cond-mat.stat-mech↗
arXiv2013

Friction due to inhomogeneous driving of coupled spins in a quantum heat engine

We consider two spin-1/2 particles with isotropic Heisenberg interaction, as the working substance of a quantum heat engine. We observe a frictional effect on the adiabatic branches of the heat cycle, which arises due to an inhomogeneous driving at a finite rate of the external magnetic field. The frictional effect is characterized by entropy production in the system and reduction in the work extracted. Corresponding to a sudden and a very slow driving, we find expressions for the lower and upper bounds of work that can be extracted on the adiabatic branches. These bounds are also confirmed with numerical simulations of the corresponding Liouville-von Neumann equation.

quant-ph↗
arXiv2013

Bounds on Thermal Efficiency from Inference

The problem of inference is applied to the process of work extraction from two constant heat capacity reservoirs, when the thermodynamic coordinates of the process are not fully specified. The information that is lacking, includes both the specific value of a temperature as well as the label of the reservoir to which it is assigned. The estimates for thermal efficiency reveal that uncertainty regarding the exact labels, reduces the maximal efficiency below the Carnot value, its minimum value being the well known Curzon-Ahlborn value. We also make an average estimate of the efficiency {\it before} the value of the temperature is revealed. It is found that if the labels are known with certainty, then in the near-equilibrium limit the efficiency scales as 1/2 of Carnot value, while if there is maximal uncertainty in the labels, then the average estimate for efficiency drops to 1/3 of Carnot value. We also suggest how infered properties of the incomplete model can be mapped to a model with complete information but with an additional source of thermodynamic irreversibility.

cond-mat.stat-mech↗
arXiv2012

Informative priors and the analogy between quantum and classical heat engines

When incomplete information about the control parameters is quantified as a prior distribution, a subtle connection emerges between quantum heat engines and their classical analogs. We study the quantum model where the uncertain parameters are the intrinsic energy scales and compare with the classical models where the intermediate temperature is the uncertain parameter. The prior distribution quantifying the incomplete information has the form $π(x)\propto 1/x$ in both the quantum and the classical models. The expected efficiency calculated in near-equilibrium limit approaches the value of one third of Carnot efficiency.

cond-mat.stat-mech↗
arXiv2012

Expected Behavior of Quantum Thermodynamic Machines with Prior Information

We estimate the expected behavior of a quantum model of heat engine when we have incomplete information about external macroscopic parameters, like magnetic field controlling the intrinsic energy scales of the working medium. We explicitly derive the prior probability distribution for these unknown parameters, $a_i, (i=1,2)$. Based on a few simple assumptions, the prior is found to be of the form $Π(a_i) \propto 1/a_i$. By calculating the expected values of various physical quantities related to this engine, we find that the expected behavior of the quantum model exhibits thermodynamic-like features. This leads us to a surprising proposal that incomplete information quantified as appropriate prior distribution can lead us to expect classical thermodynamic behavior in quantum models.

quant-ph↗
arXiv2010

A Coupled Quantum Otto Cycle

We study the 1-d isotropic Heisenberg model of two spin-1/2 systems as a quantum heat engine. The engine undergoes a four-step Otto cycle where the two adiabatic branches involve changing the external magnetic field at a fixed value of the coupling constant. We find conditions for the engine efficiency to be higher than the uncoupled model; in particular, we find an upper bound which is tighter than the Carnot bound. A new domain of parameter values is pointed out which was not feasible in the interaction-free model. Locally, each spin seems to effect the flow of heat in a direction opposite to the global temperature gradient. This seeming contradiction to the second law can be resolved in terms of local effective temperature of the spins.

quant-ph↗
arXiv2010

Universal efficiency at optimal work with Bayesian statistics

If the work per cycle of a quantum heat engine is averaged over an appropriate prior distribution for an external parameter $a$, the work becomes optimal at Curzon-Ahlborn efficiency. More general priors of the form $Π(a) \propto 1/a^γ$ yield optimal work at an efficiency which stays close to CA value, in particular near equilibrium the efficiency scales as one-half of the Carnot value. This feature is analogous to the one recently observed in literature for certain models of finite-time thermodynamics. Further, the use of Bayes' theorem implies that the work estimated with posterior probabilities also bears close analogy with the classical formula. These findings suggest that the notion of prior information can be used to reveal thermodynamic features in quantum systems, thus pointing to a new connection between thermodynamic behavior and the concept of information.

cond-mat.stat-mech↗
arXiv2009

Quantum heat engines and nonequilibrium temperature

A pair of two-level systems initially prepared in different thermal states and coupled to an external reversible work source, do not in general reach a common temperature at the end of a unitary work extraction process. We define an effective temperature for the final nonequilibrium but passive state of the bipartite quantum system and analyse its properties.

quant-ph↗
arXiv2007

Work extremum principle: Structure and function of quantum heat engines

We consider a class of quantum heat engines consisting of two subsystems interacting via a unitary transformation and coupled to two separate baths at different temperatures $T_h > T_c$. The purpose of the engine is to extract work due to the temperature difference. Its dynamics is not restricted to the near equilibrium regime. The engine structure is determined by maximizing the extracted work under various constraints. When this maximization is carried out at finite power, the engine dynamics is described by well-defined temperatures and satisfies the local version of the second law. In addition, its efficiency is bounded from below by the Curzon-Ahlborn value $1-\sqrt{T_c/T_h}$ and from above by the Carnot value $1-(T_c/T_h)$. The latter is reached|at finite power|for a macroscopic engine, while the former is achieved in the equilibrium limit $T_h\to T_c$. When the work is maximized at a zero power, even a small (few-level) engine extracts work right at the Carnot efficiency.

cond-mat.stat-mech↗
arXiv2006

Statistical mechanics of thermal contact between system and bath with long-range interactions

In this paper, we address the possibility of generalising the standard analysis of thermal contact between a sample system and a heat bath, by including long range interactions between them. As a concrete example, both system and bath are treated within the long range Ising model. For this model, we derive the equilibrium probability distribution of the energy of the sample system. Equilibrium properties of the system magnetisation and stability of the solutions is discussed. We find existence of a metastable phase below a critical temperature of the bath.

cond-mat.stat-mech↗
arXiv2005

Mutual thermal equilibrium in long-range Ising model using nonadditive entropy

Mutual equilibrium in long-range interacting systems which involve nonadditive energy, is effectively described in terms of entropy with a nonadditive composition rule. As an example, long range Ising model is considered. The generality of the term having product of the system entropies is pointed out in this framework.

cond-mat.stat-mech↗
arXiv2004

Composable entropy and deviation from macroscopic equilibrium

We formulate, under general conditions, the problem of maximisation of the total entropy of the system, assumed to be in a composable form, for fixed total value of the constrained quantity. We derive the general form of the composability function and also point out the criterion which leads to a violation of the zeroth law of thermodynamics.

cond-mat.stat-mech↗
arXiv2003

Statistical Mechanics in the Extended Gaussian Ensemble

The extended gaussian ensemble (EGE) is introduced as a generalization of the canonical ensemble. The new ensemble is a further extension of the Gaussian ensemble introduced by J. H. Hetherington [J. Low Temp. Phys. {\bf 66}, 145 (1987)]. The statistical mechanical formalism is derived both from the analysis of the system attached to a finite reservoir and from the Maximum Statistical Entropy Principle. The probability of each microstate depends on two parameters $β$ and $γ$ which allow to fix, independently, the mean energy of the system and the energy fluctuations respectively. We establish the Legendre transform structure for the generalized thermodynamic potential and propose a stability criterion. We also compare the EGE probability distribution with the $q$-exponential distribution. As an example, an application to a system with few independent spins is presented.

cond-mat.stat-mech↗
arXiv2003

Additive entropy underlying the general composable entropy prescribed by thermodynamic meta-equilibrium

We consider the meta-equilibrium state of a composite system made up of independent subsystems satisfying the additive form of external constraints, as recently discussed by Abe [Phys. Rev. E {\bf 63}, 061105 (2001)]. We derive the additive entropy $S$ underlying a composable entropy $\tilde{S}$ by identifying the common intensive variable. The simplest form of composable entropy satisfies Tsallis-type nonadditivity and the most general composable form is interpreted as a monotonically increasing funtion $H$ of this simplest form. This is consistent with the observation that the meta-equilibrium can be equivalently described by the maximum of either $H[\tilde{S}]$ or $\tilde{S}$ and the intensive variable is same in both cases.

cond-mat.stat-mech↗
arXiv2002

Zeroth law of thermodynamics and the transformation from nonextensive to extensive framework

Within the nonextensive framework, it is shown that zeroth law of thermodynamics determines not only the mapping between Lagrange multipliers and intensive variables, but also the mapping between nonextensive and extensive entropy. The form of constraints decides the form of the extensive entropy, standard averages lead to Boltzmann-Shannon-Gibbs entropy while normalised biased averages lead to Renyi entropy. The mapping between Lagrange multipliers and intensive variables is also discussed in the more general context of composable entropy.

cond-mat.stat-mech↗