Abstract
We study a Szilard engine based on a Gaussian state of a system consisting of two bosonic modes placed in a noisy channel. As the initial state of the system is taken an entangled squeezed thermal state, and the quantum work is extracted by performing a measurement on one of the two modes. We use the Markovian Kossakowski-Lindblad master equation for describing the time evolution of the open system and the quantum work definition based on the second order Rényi entropy to simulate the engine. We also study the information-work efficiency of the Szilard engine as a function of the system parameters. The efficiency is defined as the ratio of the extractable work averaged over the measurement angle and the erasure work, which is proportional to the information stored in the system. We show that the extractable quantum work increases with the temperature of the reservoir and the squeezing between the modes, average numbers of thermal photons and frequencies of the modes. The work increases also with the strength of the measurement, attaining the maximal values in the case of a heterodyne detection. The extractable work is decreasing by increasing the squeezing parameter of the noisy channel and it oscillates with the phase of the squeezed thermal reservoir. The efficiency mostly has a similar behavior with the extractable quantum work evolution. However information-work efficiency decreases with temperature, while the quantity of the extractable work increases.
Highlights
We study a Szilard engine based on a Gaussian state of a system consisting of two bosonic modes placed in a noisy channel
“Dynamics of two bosonic modes in a Gaussian noisy channel” we describe the dynamics of two bosonic modes in a Gaussian noisy channel, and in Sec
The authors have reached the conclusion that the amount of extracted work and efficiency in the classical case is larger than or equal to those in the quantum case. They explained this fact by the equilibrium configuration in the classical case in comparison with the quantum case, where only equilibrium states correspond to the thermal reservoirs
Summary
The notion of work resides in the field of classical mechanics and thermodynamics. It does not belong to in the category of observables like energy, position and momentum because it defines a process, not an instantaneous state of the system. The energy of a system is described by its Hamiltonian H(z, ) , where z is the phase space point and is the force parameter that can change the system energy in correspondence with the force protocol = { (t)|0 ≤ t ≤ τ } In this way work can be implemented by or taken from the system. The authors have reached the conclusion that the amount of extracted work and efficiency in the classical case is larger than or equal to those in the quantum case. They explained this fact by the equilibrium configuration in the classical case in comparison with the quantum case, where only equilibrium states correspond to the thermal reservoirs. Quantum Carnot cycle exhibits the same efficiency as the classical one, according to the study[33], because the quantum Carnot cycle has a calculable probability of being reversible, while in the classical case a complete cycle would require an infinitely long time, due to the fact that the ideal gas is brought quite out of equilibrium
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