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arXiv:2202.04011 · Physical Review A

Counting statistics of energy transport across squeezed thermal reservoirs

Hari Kumar Yadalam, Bijay Kumar Agarwalla, Upendra Harbola

Published Jun 30, 2022• 0 citations
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Abstract

A general formalism for computing the full counting statistics of energy exchanged between ``$N$'' squeezed thermal photon reservoirs weakly coupled to a cavity with ``$M$'' photon modes is presented. The formalism is based on the two-point measurement scheme and is applied to two simple special cases: the relaxation dynamics of a single mode cavity in contact with a single squeezed thermal photon reservoir and the steady-state energy transport between two squeezed thermal photon reservoirs coupled to a single cavity mode. Using analytical results, it is found that the short time energy exchange statistics is significantly affected by noncommutativity of the initial energy measurements with the reservoirs' squeezed states, and may lead to negative probabilities if not accounted for properly. Furthermore, it is found that for the single reservoir setup, generically there is no transient or steady-state Jarzynski-W\'ojcik energy exchange fluctuation theorem. In contrast, for the two reservoir cases, although there is no generic transient energy exchange fluctuation theorem, a steady-state energy exchange fluctuation theorem with a nonuniversal affinity is found to be valid. Statistics of energy currents are further discussed.

DOI
10.1103/physreva.105.062219

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A general formalism for computing the full counting statistics of energy exchanged between $N$'' squeezed thermal photon reservoirs weakly coupled to a cavity with MMM'' photon modes is presented. The formalism is based on the two-point measurement scheme and is applied to two simple special cases: the relaxation dynamics of a single mode cavity in contact with a single squeezed thermal photon reservoir and the steady-state energy transport between two squeezed thermal photon reservoirs coupled to a single cavity mode. Using analytical results, it is found that the short time energy exchange statistics is significantly affected by noncommutativity of the initial energy measurements with the reservoirs' squeezed states, and may lead to negative probabilities if not accounted for properly. Furthermore, it is found that for the single reservoir setup, generically there is no transient or steady-state Jarzynski-W'ojcik energy exchange fluctuation theorem. In contrast, for the two reservoir cases, although there is no generic transient energy exchange fluctuation theorem, a steady-state energy exchange fluctuation theorem with a nonuniversal affinity is found to be valid. Statistics of energy currents are further discussed.
We investigate the statistics of heat exchange between a finite system coupled to reservoir(s). We have obtained analytical results for heat fluctuation theorems in the transient regime considering the Hamiltonian dynamics of the composite system consisting of the system of interest and the heat bath(s). The system of interest is driven by an external protocol. We first derive it in the context of a single heat bath. The result is in exact agreement with known result. We then generalize the treatment to two heat baths. We further extend the study to quantum systems and show that relations similar to the classical case hold in the quantum regime. For our study we invoke von Neumann two-point projective measurement in quantum mechanics in the transient regime. The study of quantum systems follows the same lines of argument as that of the classical system, and as a result the treatment used in the latter complements that used in the former. Our result is a generalization of Jarzynski-Wòjcik heat fluctuation theorem.
Two fundamental ingredients play a decisive role in the foundations of fluctuation relations-the principle of micro-reversibility and the fact that thermal equilibrium is described by Gibbs canonical ensemble. Here we investigate the statistics of heat exchange between quantum finite system coupled to two reservoirs at temperatures Th and Tc in the transient regime. We have obtained an analytical result for quantum heat fluctuation theorem in the transient regime. We consider a composite system consisting of two different heat baths at different temperatures with an intervening medium(system of interest). The system of interest is driven by an external protocol. For our study we invoke von Neumann two point projective measurement in quantum mechanics. Our result is a generalisation of Jarzynski-Wojcik heat fluctuation theorem.
We formulate a full-counting statistics description to study energy exchange in multi-terminal junctions from weak to strong system-bath coupling regime. Our approach can describe energy transport in quantum systems that are coupled in a non-additive manner to multiple reservoirs. We derive a Redfield-type equation for the counting-field dependent reduced density operator, valid under the Markovian approximation for the baths. Under the secular approximation, we confirm that the cumulant generating function satisfies the heat exchange fluctuation theorem. Our treatment thus respects the second law of thermodynamics---though for non-additive interaction models the entropy production rate within an individual thermal bath cannot be identified. We exemplify our method on a multi-terminal two-level quantum system. We write down explicit expressions for the energy current and its noise in the additive (weak coupling) and non-additive (strong coupling) cases and verify the so-called thermodynamic uncertainty relation. Lastly, we use our formalism to describe the smallest quantum absorption refrigerator, operating through engineered reservoirs, acting cooperatively.
We build an exact framework to evaluate heat, energy, and particle transport between Gaussian reservoirs mediated by a quadratic quantum system. By combining full counting statistics with newly developed non-Markovian master equation approaches, we introduce an effective master equation whose solution can be used to generate arbitrary moments of the heat statistics for any number of reservoirs. This theory applies equally to fermionic and bosonic systems, holds at arbitrarily strong coupling, and resolves out-of-equilibrium transient dynamics determined by the system's initial state. In the steady-state, weak-coupling limit, we recover results analogous to those of the well-known Landauer-Büttiker formalism. We conclude our discussion by demonstrating an application of the method to a prototypical fermionic system. Our results uncover a regime of transient negative heat conductance contingent upon the initial system preparation, providing a clear signature of non-trivial out-of-equilibrium dynamics.
Energy exchange statistics between two bodies at different thermal equilibria obey the Jarzynski-Wójcik fluctuation theorem. The corresponding energy scale factor is the difference of the inverse temperatures associated to the bodies at equilibrium. In this work, we consider a dissipative quantum dynamics leading the quantum system towards a possibly nonthermal, asymptotic state. To generalize the Jarzynski-Wójcik theorem to nonthermal states, we identify a sufficient condition I for the existence of an energy scale factor η^{*} that is unique, finite, and time independent, such that the characteristic function of the energy exchange distribution becomes identically equal to 1 for any time. This η^{*} plays the role of the difference of inverse temperatures. We discuss the physical interpretation of the condition I, showing that it amounts to an almost complete memory loss of the initial state. The robustness of our results against quantifiable deviations from the validity of I is evaluated by experimental studies on a single nitrogen-vacancy center subjected to a sequence of laser pulses and dissipation.
We formulate a full-counting statistics description to study energy exchange in multi-terminal junctions. Our approach applies to quantum systems that are coupled either additively or non-additively (cooperatively) to multiple reservoirs. We derive a Markovian Redfield-type equation for the counting-field dependent reduced density operator. Under the secular approximation, we confirm that the cumulant generating function satisfies the heat exchange fluctuation theorem. Our treatment thus respects the second law of thermodynamics. We exemplify our formalism on a multi-terminal two-level quantum system, and apply it to realize the smallest quantum absorption refrigerator, operating through engineered reservoirs, and achievable only through a cooperative bath interaction model.