Experimental Determination of Irreversible Entropy Production in out-of-Equilibrium Mesoscopic Quantum Systems

Exploring the Thermodynamic Uncertainty Constant: Insights from a Quasi-Ideal Nano-Gas Model

In previous work, we investigated thermodynamic processes in systems at the mesoscopic level where traditional thermodynamic descriptions (macroscopic or microscopic) may not be fully adequate. The key result is that entropy in such systems does not change continuously, as in macroscopic systems, but rather in discrete steps characterized by the quantization constant β. This quantization reflects the underlying discrete nature of the collision process in low-dimensional systems and the essential role played by thermodynamic fluctuations at this scale. Thermodynamic variables conjugate to the forces, along with Glansdorff-Prigogine's dissipative variable can be discretized, enabling a mesoscopic-scale formulation of canonical commutation rules (CCRs). In this framework, measurements correspond to determining the eigenvalues of operators associated with key thermodynamic quantities. This work investigates the quantization parameter β in the CCRs using a nano-gas model analyzed through classical statistical physics. Our findings suggest that β is not an unknown fundamental constant. Instead, it emerges as the minimum achievable value derived from optimizing the uncertainty relation within the framework of our model. The expression for β is determined in terms of the ratio χ, which provides a dimensionless number that reflects the relative scales of volume and mass between entities at the Bohr (atomic level) and the molecular scales. This latter parameter quantifies the relative influence of quantum effects versus classical dynamics in a given scattering process.

Anomalous thermodynamic cost of clock synchronization

Clock synchronization is critically important in positioning, navigation and timing systems. While its performance has been intensively studied in a wide range of disciplines, much less is known for the fundamental thermodynamics of clock synchronization‒what limits the precision and how to optimize the energy cost for clock synchronization. Here, we report the first experimental investigation of two stochastic autonomous clocks synchronization, unveiling the thermodynamic relation between the entropy cost and clock synchronization in an open cavity optomechanical system. Two interacting clocks are synchronized spontaneously owing to the disparate decay rates of hybrid modes by engineering the controllable cavity-mediated dissipative coupling. The measured dependence of the degree of synchronization on the overall entropy cost exhibits an unexpected non-monotonic characteristic, while the relation between the degree of synchronization and the entropy cost for the synchronization is monotonically decreasing. The investigation of transient dynamics of clock synchronization exposes a trade-off between energy and time consumption. Our results demonstrate the possibility of clock synchronization in an effective linear system, reveal the fundamental relation between clock synchronization and thermodynamics, and have a great potential for precision measurements, distributed quantum networks, and biological science.

Geometrical Bounds on Irreversibility in Squeezed Thermal Bath

Irreversible entropy production (IEP) plays an important role in quantum thermodynamic processes. Here, we investigate the geometrical bounds of IEP in nonequilibrium thermodynamics by exemplifying a system coupled to a squeezed thermal bath subject to dissipation and dephasing, respectively. We find that the geometrical bounds of the IEP always shift in a contrary way under dissipation and dephasing, where the lower and upper bounds turning to be tighter occur in the situation of dephasing and dissipation, respectively. However, either under dissipation or under dephasing, we may reduce both the critical time of the IEP itself and the critical time of the bounds for reaching an equilibrium by harvesting the benefits of squeezing effects in which the values of the IEP, quantifying the degree of thermodynamic irreversibility, also become smaller. Therefore, due to the nonequilibrium nature of the squeezed thermal bath, the system-bath interaction energy has a prominent impact on the IEP, leading to tightness of its bounds. Our results are not contradictory with the second law of thermodynamics by involving squeezing of the bath as an available resource, which can improve the performance of quantum thermodynamic devices.

Nonequilibrium thermodynamics in cavity optomechanics

Classical thermodynamics has been a great achievement in dealing with systems that are in equilibrium or near equilibrium. As an emerging field, nonequilibrium thermodynamics provides a general framework for understanding the nonequilibrium processes, particularly in small systems that are typically far-from-equilibrium and are dominated by thermal or quantum fluctuations. Cavity optomechanical systems hold great promise among the various experimental platforms for studying nonequilibrium thermodynamics owing to their high controllability, excellent mechanical performance, and ability to operate deep in the quantum regime. Here, we present an overview of the recent advances in nonequilibrium thermodynamics with cavity optomechanical systems. The experimental results in entropy production assessment, fluctuation theorems, heat transfer, and heat engines are highlighted.

Qubit thermodynamics far from equilibrium: Two perspectives about the nature of heat and work in the quantum regime

Considering an entropy-based division of energy transferred into heat and work, we develop an alternative theoretical framework for the thermodynamic analysis of two-level systems. When comparing these results with those obtained using the standard definitions of these quantities, we observe the appearance of a different term of work, which represents the energy cost of rotating the Bloch vector in the presence of the external field that defines the local Hamiltonian. Additionally, we obtain explicit expressions for the temperature, the heat capacity, and the internal entropy production of the system in both paradigms. In order to illustrate our findings we study, from both perspectives, matter-radiation interaction processes for two different systems.

Entropy production and Onsager reciprocal relations describing the relaxation to equilibrium in stochastic thermodynamics

We study the relation between stochastic thermodynamics and nonequilibrium thermodynamics by evaluating the entropy production and the relation between fluxes and forces in a harmonic system with N particles in contact with N different reservoirs. We suppose that the system is in a nonequilibrium stationary state in a first phase and we study the relaxation to equilibrium in a second phase. During this relaxation, we can identify the linear relation between fluxes and forces satisfying the Onsager reciprocity and we obtain a nonlinear expression for the entropy production. Only when forces and fluxes are small does the entropic production turn into a quadratic form in the forces, as predicted by the Onsager theory.

Quantum measurement arrow of time and fluctuation relations for measuring spin of ultracold atoms

The origin of macroscopic irreversibility from microscopically time-reversible dynamical laws—often called the arrow-of-time problem—is of fundamental interest in both science and philosophy. Experimentally probing such questions in quantum theory requires systems with near-perfect isolation from the environment and long coherence times. Ultracold atoms are uniquely suited to this task. We experimentally demonstrate a striking parallel between the statistical irreversibility of wavefunction collapse and the arrow of time problem in the weak measurement of the quantum spin of an atomic cloud. Our experiments include statistically rare events where the arrow of time is inferred backward; nevertheless we provide evidence for absolute irreversibility and a strictly positive average arrow of time for the measurement process, captured by a fluctuation theorem. We further demonstrate absolute irreversibility for measurements performed on a quantum many-body entangled wavefunction—a unique opportunity afforded by our platform—with implications for studying quantum many-body dynamics and quantum thermodynamics.

Irreversibility in quantum measurements shares conceptual links with statistical and thermodynamical irreversibility. Here, the authors are able to operationally associate an "arrow of time” to quantum weak measurements, testing it experimentally on a cloud of ultracold atoms.

Experimental Test of the 1/τ-Scaling Entropy Generation in Finite-Time Thermodynamics

The finite-time dynamics, apart from its fundamental importance in nonequilibrium thermodynamics, is of great significance in designing heat engine cycles. We build an experimental apparatus to test the predicted long-time 1/τ scaling of the irreversible entropy generation in the finite-time (τ) thermodynamic process by compressing dry air in a temperature-controlled water bath. We present the first direct experimental validation of the scaling, utilized in many finite-time thermodynamic models at the long-time regime. The experimental data also demonstrate a clear deviation from the scaling at the short-time regime. We show the optimal control scheme to minimize the irreversible entropy generation in finite-time process. Such optimization shall bring new insight to the practical design of heat engine cycles.

Experimental Assessment of Entropy Production in a Continuously Measured Mechanical Resonator

The information on a quantum process acquired through measurements plays a crucial role in the determination of its nonequilibrium thermodynamic properties. We report on the experimental inference of the stochastic entropy production rate for a continuously monitored mesoscopic quantum system. We consider an optomechanical system subjected to continuous displacement Gaussian measurements and characterize the entropy production rate of the individual trajectories followed by the system in its stochastic dynamics, employing a phase-space description in terms of the Wigner entropy. Owing to the specific regime of our experiment, we are able to single out the informational contribution to the entropy production arising from conditioning the state on the measurement outcomes. Our experiment embodies a significant step towards the demonstration of full-scale control of fundamental thermodynamic processes at the mesoscopic quantum scale.

Enhanced Energy Transfer to an Optomechanical Piston from Indistinguishable Photons

Thought experiments involving gases and pistons, such as Maxwell's demon and Gibbs' mixing, are central to our understanding of thermodynamics. Here, we present a quantum thermodynamic thought experiment in which the energy transfer from two photonic gases to a piston membrane grows quadratically with the number of photons for indistinguishable gases, while it grows linearly for distinguishable gases. This signature of bosonic bunching may be observed in optomechanical experiments, highlighting the potential of these systems for the realization of thermodynamic thought experiments in the quantum realm.

Out-of-equilibrium quantum thermodynamics in the Bloch sphere: Temperature and internal entropy production

An explicit expression for the temperature of an open two-level quantum system is obtained as a function of local properties under the hypothesis of weak interaction with the environment. This temperature is defined for both equilibrium and out-of-equilibrium states and coincides with the environment temperature if the system reaches thermal equilibrium with a heat reservoir. Additionally, we show that within this theoretical framework the total entropy production can be partitioned into two contributions: one due to heat transfer and another, associated to internal irreversibilities, related to the loss of internal coherence by the qubit. The positiveness of the heat capacity is established, as well as its consistency with the well-known results at thermal equilibrium. We apply these concepts to two different systems and show that they behave in analogous ways as their classical counterparts.

Gaussian Thermal Operations and The Limits of Algorithmic Cooling

The study of thermal operations allows one to investigate the ultimate possibilities of quantum states and of nanoscale thermal machines. Whilst fairly general, these results typically do not apply to continuous variable systems and do not take into account that, in many practically relevant settings, system-environment interactions are effectively bilinear. Here we tackle these issues by focusing on Gaussian quantum states and channels. We provide a complete characterization of the most general Gaussian thermal operation acting on an arbitrary number of bosonic modes, which turn out to be all embeddable in a Markovian dynamics, and derive necessary and sufficient conditions for state transformations under such operations in the single-mode case, encompassing states with nonzero coherence in the energy eigenbasis (i.e., squeezed states). Our analysis leads to a no-go result for the technologically relevant task of algorithmic cooling: We show that it is impossible to reduce the entropy of a system coupled to a Gaussian environment below its own or the environmental temperature, by means of a sequence of Gaussian thermal operations interspersed by arbitrary (even non-Gaussian) unitaries. These findings establish fundamental constraints on the usefulness of Gaussian resources for quantum thermodynamic processes.

Entropy production as a tool for characterizing nonequilibrium phase transitions

Nonequilibrium phase transitions can be typified in a similar way to equilibrium systems, for instance, by the use of the order parameter. However, this characterization hides the irreversible character of the dynamics as well as its influence on the phase transition properties. Entropy production has been revealed to be an important concept for filling this gap since it vanishes identically for equilibrium systems and is positive for the nonequilibrium case. Based on distinct and general arguments, the characterization of phase transitions in terms of the entropy production is presented. Analysis for discontinuous and continuous phase transitions has been undertaken by taking regular and complex topologies within the framework of mean-field theory (MFT) and beyond the MFT. A general description of entropy production portraits for Z_{2} ("up-down") symmetry systems under the MFT is presented. Our main result is that a given phase transition, whether continuous or discontinuous has a specific entropy production hallmark. Our predictions are exemplified by an icon system, perhaps the simplest nonequilibrium model presenting an order-disorder phase transition and spontaneous symmetry breaking: the majority vote model. Our work paves the way to a systematic description and classification of nonequilibrium phase transitions through a key indicator of system irreversibility.