Quantum heat engines, the second law and Maxwell's daemon

Abstract

We introduce a class of quantum heat engines which consists of two-energy-eigenstate systems, the simplest of quantum mechanical systems, undergoing quantum adiabatic processes and energy exchanges with heat baths, respectively, at different stages of a cycle. Armed with this class of heat engines and some interpretation of heat transferred and work performed at the quantum level, we are able to clarify some important aspects of the second law of thermodynamics. In particular, it is not sufficient to have the heat source hotter than the sink, but there must be a minimum temperature difference between the hotter source and the cooler sink before any work can be extracted through the engines. The size of this minimum temperature difference is dictated by that of the energy gaps of the quantum engines involved. Our new quantum heat engines also offer a practical way, as an alternative to Szilard's engine, to physically realise Maxwell's daemon. Inspired and motivated by the Rabi oscillations, we further introduce some modifications to the quantum heat engines with single-mode cavities in order to, while respecting the second law, extract more work from the heat baths than is otherwise possible in thermal equilibria. Some of the results above are also generalisable to quantum heat engines of an infinite number of energy levels including 1-D simple harmonic oscillators and 1-D infinite square wells.

Thermodynamics of complexity and pattern manipulation

“…Our results have meaning in any physical framework that: 1. provides a way of mapping random variables to physical states, and 2. has definitions of heat and work exchange, such that any allowed reconfiguration of these mapped states has a work cost bounded by Landauer's principle, as applied to the associated random variables. A list of such frameworks satisfying these criteria includes the trajectory formalism [21][22][23][24][25][26] (see Physical Example in the Technical Appendix), the resource theory of thermodynamics (e.g. [7,8]), single-shot statistical mechanics (e.g.…”

“…A list of such frameworks satisfying these criteria includes the trajectory formalism [21][22][23][24][25][26] (see Physical Example in the Technical Appendix), the resource theory of thermodynamics (e.g. [7,8]), single-shot statistical mechanics (e.g.…”

Non-Hermitian heat engine with all-quantum-adiabatic-process cycle

“…According to the definition in the Refs. [30,9,10], our calculations indicate that such an engine can operate at Otto efficiency…”

“…For a traditional (Hermitian) QHE, the temperature of a quantum working medium is introduced based on the thermalization assumption [9,10,30,36], that is, the working medium has the same distribution of occupation probability as the heat bath in thermodynamic equilibrium. Then for such a small quantum system, the probability distribution is related to a parameter called spectral temperature.…”

“…Due to the quantum properties of the working medium, or the effects of the quantum heat bath, some unusual and exotic phenomena have been manifested by considering and using a squeezed reservoir [24,25], quantum coherence [23], or coupled spins [26,27,28,29]. Moreover, via constructing a QHE which is a two-level quantum system and undergoes quantum adiabatic process and energy exchanges with heat baths at different stages in a work cycle, some important aspects of the second law of thermodynamics have been clarified by Kieu [30]. Very recently, many other investigations have been carried out and demonstrated about the Carnot statement of the second law of thermodynamics and the quantum Jarzynski equality in quantum systems described by pseudo-Hermitian Hamiltonians [31].…”