Quantum Approach to Classical Thermodynamics and Optimization

A Imparato, Nicholas Chancellor, G De Chiara

Rolando D. Somma, Cristian D. Batista, Gerardo Ortíz

We present two approaches to study the thermodynamic properties of d -dimensional classical systems in equilibrium. In the first approach we reduce this problem to the computation of the ground state properties of a d -dimensional quantum model. This classical-to-quantum mapping allows us to extend the scope of standard optimization methods by unifying them under a general framework. Particularly, we extend the quantum annealing method to study classical systems at finite temperatures. We derive the rates to assure convergence to the optimal thermodynamic state using the adiabatic theorem of quantum mechanics. In the second approach we present a quantum algorithm that performs numerical integration and computes, for example, the partition function of the system under study. We show that this quantum algorithm provides a quadratic speed-up with respect to the classical algorithm that samples with the uniform distribution and computes physical quantities of interest. Other quantum strategies, as well as their potential speed-up, are also discussed.

Eitan Geva, Ronnie Kosloff

The finite time performance of quantum heat engines has been examined with emphasis on the classical, high temperature, limit. Two basic engine models were studied, differing by their consistency of working fluid: the harmonic engine, consisting of noninteracting harmonic oscillators, and the spin-j engine, consisting of noninteracting spin-j subsystems. The two models represent two distinct types of engines, with bounded vs unbounded Hamiltonians, and with creation and annihilation operators of the Fermionic vs the Bosonic type. The analysis is based on the time derivatives of the first and second laws of thermodynamics. Explicit relations linking quantum observables to thermodynamic quantities are utilized. The dynamics of the engines was modeled by the semigroup approach. The engines were optimized with respect to various target functions: power, entropy production, and efficiency, while subject to finite cycle duration. The main strategy of optimization was based on the Euler–Lagrange equation, and is similar to that previously applied by Salamon and Nitzan for the investigation of Newtonian engines [J. Chem. Phys. 74, 3546 (1981)]. The optimal cycles obtained at the classical limit are not of the Curzon–Ahlborn type, i.e., the internal temperature along the thermal branches is not constant. This result is in conflict with Newtonian thermodynamics, where the optimal cycles are of the Curzon–Ahlborn type. Nonetheless, some of the main features of Newtonian thermodynamics, such as the Curzon–Ahlborn efficiency at maximum power, are reproduced at the classical limit. This makes it possible to establish a ‘‘thermodynamic correspondence principle.’’ This principle asserts that the phenomenological Newtonian thermodynamic approach provides an asymptote of a theory based upon the more fundamental semigroup quantum approach. It is argued that the asymptotic nature of Newtonian thermodynamics is twofold since its validity is restricted by two demands: that of high temperatures and that of proximity to equilibrium.

O. N. Golubjeva, Alexander D. Sukhanov, Umanskaja Zh.V.

Gershon Kurizki, Nilakantha Meher, Avijit Misra +2 more

A. de Oliveira, M. C. de Oliveira

At the heart of quantum thermodynamics lies a fundamental question about what is genuine "quantum" in quantum heat engines and how to seek this quantumness, so that thermodynamical tasks could be performed more efficiently compared with classical protocols. Here, using the concept of P-representability, we define a function called classicality, which quantifies the degree of non-classicality of bosonic modes. This function allows us to explore the role of non-classicality in quantum heat engines and design optimal protocols for work extraction. For two specific cycles, a quantum Otto and a generalised one, we show that non-classicality is a fundamental resource for performing thermodynamic tasks more efficiently.