Philipp Strasberg

Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping

We propose a method to study the thermodynamic behaviour of small systems beyond the weak coupling and Markovian approximation, which is different in spirit from conventional approaches. The idea is to redefine the system and environment such that the effective, redefined system is again coupled weakly to Markovian residual baths and thus, allows to derive a consistent thermodynamic framework for this new system-environment partition. To achieve this goal we make use of the reaction coordinate mapping, which is a general method in the sense that it can be applied to an arbitrary (quantum or classical and even time-dependent) system coupled linearly to an arbitrary number of harmonic oscillator reservoirs. The core of the method relies on an appropriate identification of a part of the environment (the reaction coordinate), which is subsequently included as a part of the system. We demonstrate the power of this concept by showing that non-Markovian effects can significantly enhance the steady state efficiency of a three-level-maser heat engine, even in the regime of weak system-bath coupling. Furthermore, we show for a single electron transistor coupled to vibrations that our method allows one to justify master equations derived in a polaron transformed reference frame.

Stochastic thermodynamics in the strong coupling regime: An unambiguous approach based on coarse graining

We consider a classical and possibly driven composite system X⊗Y weakly coupled to a Markovian thermal reservoir R so that an unambiguous stochastic thermodynamics ensues for X⊗Y. This setup can be equivalently seen as a system X strongly coupled to a non-Markovian reservoir Y⊗R. We demonstrate that only in the limit where the dynamics of Y is much faster than X, our unambiguous expressions for thermodynamic quantities, such as heat, entropy, or internal energy, are equivalent to the strong coupling expressions recently obtained in the literature using the Hamiltonian of mean force. By doing so, we also significantly extend these results by formulating them at the level of instantaneous rates and by allowing for time-dependent couplings between X and its environment. Away from the limit where Y evolves much faster than X, previous approaches fail to reproduce the correct results from the original unambiguous formulation, as we illustrate numerically for an underdamped Brownian particle coupled strongly to a non-Markovian reservoir.

Strong suppression of shot noise in a feedback-controlled single-electron transistor

Feedback control of quantum mechanical systems is rapidly attracting attention not only due to fundamental questions about quantum measurements, but also because of its novel applications in many fields in physics. Quantum control has been studied intensively in quantum optics but progress has recently been made in the control of solid-state qubits as well. In quantum transport only a few active and passive feedback experiments have been realized on the level of single electrons, although theoretical proposals exist. Here we demonstrate the suppression of shot noise in a single-electron transistor using an exclusively electronic closed-loop feedback to monitor and adjust the counting statistics. With increasing feedback response we observe a stronger suppression and faster freezing of charge current fluctuations. Our technique is analogous to the generation of squeezed light with in-loop photodetection as used in quantum optics. Sub-Poisson single-electron sources will pave the way for high-precision measurements in quantum transport similar to optical or optomechanical equivalents.

Second laws for an information driven current through a spin valve.

We propose a physically realizable Maxwells demon device using a spin valve interacting unitarily for a short time with electrons placed on a tape of quantum dots, which is thermodynamically equivalent to the device introduced by Mandal and Jarzynski [D. Mandal and C. Jarzynski, Proc. Natl. Acad. Sci. USA 109, 11641 (2012)]. The model is exactly solvable and we show that it can be equivalently interpreted as a Brownian ratchet demon. We then consider a measurement-based discrete feedback scheme, which produces identical system dynamics, but possesses a different second law inequality. We show that the second law for discrete feedback control can provide a smaller, equal, or larger bound on the maximum extractable work as compared to the second law involving the tape of bits. Finally, we derive an effective master equation governing the system evolution for Poisson distributed bits on the tape (or measurement times, respectively) and we show that its associated entropy production rate contains the same physical statement as the second law involving the tape of bits.

Thermodynamics of quantum-jump-conditioned feedback control

We consider open quantum systems weakly coupled to thermal reservoirs and subjected to quantum feedback operations triggered with or without delay by monitored quantum jumps. We establish a thermodynamic description of such systems and analyze how the first and second law of thermodynamics are modified by the feedback. We apply our formalism to study the efficiency of a qubit subjected to a quantum feedback control and operating as a heat pump between two reservoirs. We also demonstrate that quantum feedbacks can be used to stabilize coherences in nonequilibrium stationary states which in some cases may even become pure quantum states.

Thermodynamics of stochastic Turing machines

In analogy to Brownian computers we explicitly show how to construct stochastic models which mimic the behavior of a general-purpose computer (a Turing machine). Our models are discrete state systems obeying a Markovian master equation, which are logically reversible and have a well-defined and consistent thermodynamic interpretation. The resulting master equation, which describes a simple one-step process on an enormously large state space, allows us to thoroughly investigate the thermodynamics of computation for this situation. Especially in the stationary regime we can well approximate the master equation by a simple Fokker-Planck equation in one dimension. We then show that the entropy production rate at steady state can be made arbitrarily small, but the total (integrated) entropy production is finite and grows logarithmically with the number of computational steps.

Stochastic thermodynamics based on incomplete information: generalized Jarzynski equality with measurement errors with or without feedback

In the derivation of fluctuation relations, and in stochastic thermodynamics in general, it is tacitly assumed that we can measure the system perfectly, i.e., without measurement errors. We here demonstrate for a driven system immersed in a single heat bath, for which the classic Jarzynski equality

From quantum heat engines to laser cooling: Floquet theory beyond the Born–Markov approximation

\langle e^{-\beta(W-\Delta F)}\rangle = 1

Controlling the Stability of Steady States in Continuous Variable Quantum Systems

holds, how to relax this assumption. Based on a general measurement model akin to Bayesian inference we derive a general expression for the fluctuation relation of the measured work and we study the case of an overdamped Brownian particle and of a two-level system in particular. We then generalize our results further and incorporate feedback in our description. We show and argue that, if measurement errors are fully taken into account by the agent who controls and observes the system, the standard Jarzynski-Sagawa-Ueda relation should be formulated differently. We again explicitly demonstrate this for an overdamped Brownian particle and a two-level system where the fluctuation relation of the measured work differs significantly from the efficacy parameter introduced by Sagawa and Ueda. Instead, the generalized fluctuation relation under feedback control,

Thermodynamics of a Physical Model Implementing a Maxwell Demon

\langle e^{-\beta(W-\Delta F)-I}\rangle = 1