Thermodynamic uncertainty relation for biomolecular processes

Improved estimation for energy dissipation in biochemical oscillations

Biochemical oscillations, regulating the timing of life processes, need consume energy to achieve good performance on crucial functions, such as high accuracy of phase period and high sensitivity to external signals. However, it is a great challenge to precisely estimate the energy dissipation in such systems. Here, based on the stochastic normal form theory (SNFT), we calculate the Pearson correlation coefficient between the oscillatory amplitude and phase, and a trade-off relation between transport efficiency and phase sensitivity can then be derived, which serves as a tighter form than the estimator resulting from the conventional thermodynamic uncertainty relation (TUR). Our findings demonstrate that a more precise energy dissipation estimation can be obtained by enhancing the sensitivity of the biochemical oscillations. Moreover, the internal noise and amplitude power effects have also been discovered.

A model of minimal entropy generation for cytoskeletal transport systems with multiple interacting motors

We study the steady-state rate of entropy generation for multiple interacting particles. The description used is based on the partially asymmetric exclusion process in a lattice with periodic boundary conditions. Our methodology shows that in the steady-state, the rate of entropy generation is directly proportional to the bulk drift and the applied driving force. Since in many cases the driving force is unknown or hard to determine. We circumvent this by deriving a lower bound for the entropy, resulting in an extended thermodynamic uncertainty relation for the asymmetric simple exclusion process. We systematically compared this bound with the actual entropy generation. Thus, we identify the force regimes, and particles' density conditions where the entropy bound derived from this extended thermodynamic uncertainty relation is meaningful.

Characterizing the Asymmetry in Hardness between Synthesis and Destruction of Heteropolymers

We present a simple model describing the assembly and disassembly of heteropolymers consisting of two types of monomers A and B. We prove that no matter how we manipulate the concentrations of A and B, it takes longer than the exponential function of d to synthesize a fixed amount of the desired heteropolymer, where d is the number of A-B connections. We also prove the decomposition time is linear for chain length n. When d is proportional to n, synthesis and destruction have an exponential asymmetry. Our findings may facilitate research on the more general asymmetry of operational hardness.

Verification of Information Thermodynamics in a Trapped Ion System

Information thermodynamics has developed rapidly over past years, and the trapped ions, as a controllable quantum system, have demonstrated feasibility to experimentally verify the theoretical predictions in the information thermodynamics. Here, we address some representative theories of information thermodynamics, such as the quantum Landauer principle, information equality based on the two-point measurement, information-theoretical bound of irreversibility, and speed limit restrained by the entropy production of system, and review their experimental demonstration in the trapped ion system. In these schemes, the typical physical processes, such as the entropy flow, energy transfer, and information flow, build the connection between thermodynamic processes and information variation. We then elucidate the concrete quantum control strategies to simulate these processes by using quantum operators and the decay paths in the trapped-ion system. Based on them, some significantly dynamical processes in the trapped ion system to realize the newly proposed information-thermodynamic models is reviewed. Although only some latest experimental results of information thermodynamics with a single trapped-ion quantum system are reviewed here, we expect to find more exploration in the future with more ions involved in the experimental systems.

Coherence of oscillations in the weak-noise limit

In a noisy environment, oscillations lose their coherence, which can be characterized by a quality factor. We determine this quality factor for oscillations arising from a driven Fokker-Planck dynamics along a periodic one-dimensional potential analytically in the weak-noise limit. With this expression, we can prove for this continuum model the analog of an upper bound that has been conjectured for the coherence of oscillations in discrete Markov network models. We show that our approach can also be adapted to motion along a noisy two-dimensional limit cycle. Specifically, we apply our scheme to the noisy Stuart-Landau oscillator and the thermodynamically consistent Brusselator as a simple model for a chemical clock. Our approach thus complements the fairly sophisticated extant general framework based on techniques from Hamilton-Jacobi theory with which we compare our results numerically.

Collective Drifts in Vibrated Granular Packings: The Interplay of Friction and Structure

We simulate vertically shaken dense granular packings with horizontal periodic boundary conditions. A coordinated translating motion of the whole medium emerges when the horizontal symmetry is broken by disorder or defects in the packing and the shaking is weak enough to conserve the structure. We argue that such a drift originates in the interplay between structural symmetry breaking and frictional forces transmitted by the vibrating plate. A nonlinear ratchet model with stick slips reproduces many faces of the phenomenon. The collective motion discussed here underlies phenomena observed recently with vibrofluidized granular materials, such as persistent rotations and anomalous diffusion.

Thermodynamics of Precision in Markovian Open Quantum Dynamics

The thermodynamic and kinetic uncertainty relations indicate trade-offs between the relative fluctuation of observables and thermodynamic quantities such as dissipation and dynamical activity. Although these relations have been well studied for classical systems, they remain largely unexplored in the quantum regime. In this Letter, we investigate such trade-off relations for Markovian open quantum systems whose underlying dynamics are quantum jumps, such as thermal processes and quantum measurement processes. Specifically, we derive finite-time lower bounds on the relative fluctuation of both dynamical observables and their first passage times for arbitrary initial states. The bounds imply that the precision of observables is constrained not only by thermodynamic quantities but also by quantum coherence. We find that the product of the relative fluctuation and entropy production or dynamical activity is enhanced by quantum coherence in a generic class of dissipative processes of systems with nondegenerate energy levels. Our findings provide insights into the survival of the classical uncertainty relations in quantum cases.

Operationally accessible uncertainty relations for thermodynamically consistent semi-Markov processes

Semi-Markov processes generalize Markov processes by adding temporal memory effects as expressed by a semi-Markov kernel. We recall the path weight for a semi-Markov trajectory and the fact that thermodynamic consistency in equilibrium imposes a crucial condition called direction-time independence for which we present an alternative derivation. We prove a thermodynamic uncertainty relation that formally resembles the one for a discrete-time Markov process. The result relates the entropy production of the semi-Markov process to mean and variance of steady-state currents. We prove a further thermodynamic uncertainty relation valid for semi-Markov descriptions of coarse-grained Markov processes that emerge by grouping states together. A violation of this inequality can be used as an inference tool to conclude that a given semi-Markov process cannot result from coarse graining an underlying Markov one. We illustrate these results with representative examples.

Classical Pendulum Clocks Break the Thermodynamic Uncertainty Relation

The thermodynamic uncertainty relation expresses a seemingly universal trade-off between the cost for driving an autonomous system and precision in any output observable. It has so far been proven for discrete systems and for overdamped Brownian motion. Its validity for the more general class of underdamped Brownian motion, where inertia is relevant, was conjectured based on numerical evidence. We now disprove this conjecture by constructing a counterexample. Its design is inspired by a classical pendulum clock, which uses an escapement to couple the motion of an oscillator to regulate the motion of another degree of freedom (a "hand") driven by an external force. Considering a thermodynamically consistent, discrete model for an escapement mechanism, we first show that the oscillations of an underdamped harmonic oscillator in thermal equilibrium are sufficient to break the thermodynamic uncertainty relation. We then show that this is also the case in simulations of a fully continuous underdamped system with a potential landscape that mimics an escaped pendulum.

Thermodynamic uncertainty relation for quantum first-passage processes

We derive a thermodynamic uncertainty relation for first passage processes in quantum Markov chains. We consider first passage processes that stop after a fixed number of jump events, which contrasts with typical quantum Markov chains which end at a fixed time. We obtain bounds for the observables of the first passage processes in quantum Markov chains by the Loschmidt echo, which quantifies the extent of irreversibility in quantum many-body systems. Considering a particular case, we show that the lower bound corresponds to the quantum Fisher information, which plays a fundamental role in uncertainty relations in quantum systems. Moreover, considering classical dynamics, our bound reduces to a thermodynamic uncertainty relation for classical first passage processes.

The role of entropy gains in the exciton separation in organic solar cells

In organic solar cell (OSC), the lower dielectric constant of organic semiconductor material induces a strong Coulomb attraction between electron-hole pairs, which leads to a low exciton separation efficiency, especially the charge transfer (CT) state. The CT state formed at the electron-donor (D) and electron-acceptor (A) interface is regarded as an unfavorable property of organic photovoltaic devices. Since the OSC works in a nonzero temperature condition, the entropy effect would be one of the main reasons to overcome the Coulomb energy barrier and must be taken into account. In this review, we review the present understanding of the entropy-driven charge separation and describe how factors such as the dimensionality of the organic semiconductor, energy disorder effect, the morphology of the active layer, and the nonequilibrium effect affect the entropy contribution in compensating the Coulomb dissociation barrier for CT exciton separation and charge generation process. We focus on the investigation of the entropy effect on exciton dissociation mechanism from both theoretical and experimental aspects, which provides pathways for understanding the underlying mechanisms of exciton separation and further enhancing the efficiency of OSCs. This article is protected by copyright. All rights reserved.

Thermodynamic uncertainty relation for quantum work distribution: Exact case study for a perturbed oscillator

Recently, some general relations have been intensively investigated in nonequilibrium mesoscopic systems. In particular, the thermodynamic uncertainty relation (TUR) provides a general bound of the precision for the fluctuation of some currents in terms of the corresponding entropy production. On the other hand, the fluctuation of the work performed is also a significant quantity, which is supposed to satisfy TUR under some conditions, such as symmetric driving protocol. In this paper, we analytically show that the TUR holds for the work performed on an externally perturbed quantum harmonic oscillator interacting with multiple reservoirs in full quantum regime. In this manner, we evaluate how the noncommutativity affects the thermodynamic precision. We also explore its experimental accessibility.

Universal bounds on cooling power and cooling efficiency for autonomous absorption refrigerators

For steady-state autonomous absorption refrigerators operating in the linear response regime, we show that there exists a hierarchy between the relative fluctuation of currents for cold, hot, and work terminals. Our proof requires the Onsager reciprocity relation along with the refrigeration condition that sets the direction of the mean currents for each terminal. As a consequence, the universal bounds on the mean cooling power, obtained following the thermodynamic uncertainty relations, follow a hierarchy. Interestingly, within this hierarchy, the tightest bound is given in terms of the work current fluctuation. Furthermore, the relative uncertainty hierarchy introduces a bound on cooling efficiency that is tighter than the bound obtained from the thermodynamic uncertainty relations. Interestingly, all of these bounds saturate in the tight-coupling limit. We test the validity of our results for two paradigmatic absorption refrigerator models: (i) a four-level working fluid and (ii) a two-level working fluid, operating in the weak (additive) and strong (multiplicative) system-bath interaction regimes, respectively.

Cycle Flux Ranking of Network Analysis in Quantum Thermal Devices

Manipulating quantum thermal transport relies on uncovering the principle working cycles of quantum devices. Here we introduce the cycle flux ranking of network analysis to nonequilibrium thermal devices characterized as a quantum-transition network. To excavate the principal mechanism out of complex transport behaviors, we decompose the network into cycle trajectories, collect the cycle fluxes by algebraic graph theory, and select top-ranked cycle fluxes, i.e., the cycle trajectories with highest probabilities. We exemplify the cycle flux ranking in typical quantum device models, e.g., a thermal-drag spin-Seebeck pump and a quantum thermal transistor. Top-ranked cycle trajectories indeed elucidate the principal working mechanisms. Therefore, cycle flux ranking provides an alternative perspective that naturally describes the working cycle corresponding to the main functionality of quantum thermal devices, which would further guide the device optimization with desired performance.

Experimental Verification of Dissipation-Time Uncertainty Relation

Dissipation is vital to any cyclic process in realistic systems. Recent research focus on nonequilibrium processes in stochastic systems has revealed a fundamental trade-off, called dissipation-time uncertainty relation, that entropy production rate associated with dissipation bounds the evolution pace of physical processes [Phys. Rev. Lett. 125, 120604 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.120604]. Following the dissipative two-level model exemplified in the same Letter, we experimentally verify this fundamental trade-off in a single trapped ultracold ^{40}Ca^{+} ion using elaborately designed dissipative channels, along with a postprocessing method developed in the data analysis, to build the effective nonequilibrium stochastic evolutions for the energy transfer between two heat baths mediated by a qubit. Since the dissipation-time uncertainty relation imposes a constraint on the quantum speed regarding entropy flux, our observation provides the first experimental evidence confirming such a speed restriction from thermodynamics on quantum operations due to dissipation, which helps us further understand the role of thermodynamical characteristics played in quantum information processing.

Bounds on fluctuations for machines with broken time-reversal symmetry: A linear response study

For a generic class of machines with broken time-reversal symmetry we show that in the linear response regime the relative fluctuation of the sum of output currents for time-forward and time-reversed processes is always lower bounded by the corresponding relative fluctuation of the sum of input currents. This bound is received when the same operating condition, for example, engine, refrigerator, or pump, is imposed on both the forward and the reversed processes. As a consequence, universal upper and lower bounds for the ratio between fluctuations of output and input current are obtained. Furthermore, we establish an important connection between our results and the recently obtained generalized thermodynamic uncertainty relations for time-reversal symmetry-broken systems. We illustrate these findings for two different types of machines: (1) a steady-state three-terminal quantum thermoelectric setup in presence of an external magnetic field and (2) a periodically driven classical Brownian heat engine.

Effects of the non-Markovianity and non-Gaussianity of active environmental noises on engine performance

An active environment is a reservoir containing active materials, such as bacteria and Janus particles. Given the self-propelled motion of these materials, powered by chemical energy, an active environment has unique, nonequilibrium environmental noise. Recently, studies on engines that harvest energy from active environments have attracted a great deal of attention because the theoretical and experimental findings indicate that these engines outperform conventional ones. Studies have explored the features of active environments essential for outperformance, such as the non-Gaussian or non-Markovian nature of the active noise. We systematically study the effects of the non-Gaussianity and non-Markovianity of active noise on engine performance. We show that non-Gaussianity is irrelevant to the performance of an engine driven by any linear force (including a harmonic trap) regardless of time dependency, whereas non-Markovianity is relevant. However, for a system driven by a general nonlinear force, both non-Gaussianity and non-Markovianity enhance engine performance. Also, the memory effect of an active reservoir should be considered when fabricating a cyclic engine.

Optimizing thermodynamic cycles with two finite-sized reservoirs

We study the nonequilibrium thermodynamics of a heat engine operating between two finite-sized reservoirs with well-defined temperatures. Within the linear response regime, it is found that the uniform temperature of the two reservoirs at final time τ is bounded from below by the entropy production σ_{min}∝1/τ. We discover a general power-efficiency tradeoff depending on the ratio of heat capacities (γ) of the reservoirs for the engine, and a universal efficiency at maximum average power of the engine for arbitrary γ is obtained. For practical purposes, the operation protocol of an ideal gas heat engine to achieve the optimal performance associated with σ_{min} is demonstrated. Our findings can be used to develop a general optimization scenario for thermodynamic cycles with finite-sized reservoirs in real-world circumstances.

Generalized virial equation for nonlinear multiplicative Langevin dynamics: Application to laser-cooled atoms

The virial theorem, and the equipartition theorem in the case of quadratic degrees of freedom, are handy constraints on the statistics of equilibrium systems. Their violation is instrumental in determining how far from equilibrium a driven system might be. We extend the virial theorem to nonequilibrium conditions for Langevin dynamics with nonlinear friction and multiplicative noise. In particular, we generalize it for confined laser-cooled atoms in the semiclassical regime. The resulting relation between the lowest moments of the atom position and velocity allows to measure in experiments how dissipative the cooling mechanism is. Moreover, its violation can reveal the departure from a strictly harmonic confinement or from the semiclassical regime.

Obtaining efficient thermal engines from interacting Brownian particles under time-periodic drivings

We introduce an alternative route for obtaining reliable cyclic engines, based on two interacting Brownian particles under time-periodic drivings which can be used as a work-to-work converter or a heat engine. Exact expressions for the thermodynamic fluxes, such as power and heat, are obtained using the framework of stochastic thermodynamic. We then use these exact expression to optimize the driving protocols with respect to output forces, their phase difference. For the work-to-work engine, they are solely expressed in terms of Onsager coefficients and their derivatives, whereas nonlinear effects start to play a role since the particles are at different temperatures. Our results suggest that stronger coupling generally leads to better performance, but careful design is needed to optimize the external forces.

Origin of loose bound of the thermodynamic uncertainty relation in a dissipative two-level quantum system

Thermodynamic uncertainty relations (TURs), originally discovered for classical systems, dictate the tradeoff between dissipation and fluctuations of irreversible current, specifying a minimal bound that constrains the two quantities. In a series of efforts to extend the relation to the one under more generalized conditions, it has been noticed that the bound is less tight in open quantum processes. To study the origin of the loose bounds, we consider an external field-driven transition dynamics of a two-level quantum system weakly coupled to the bosonic bath as a model of an open quantum system. The model makes it explicit that the imaginary part of quantum coherence, which contributes to dissipation to the environment, is responsible for loosening the TUR bound by suppressing the relative fluctuations in the irreversible current of transitions, whereas the real part of the coherence tightens it. Our study offers a better understanding of how quantum nature affects the TUR bound.

Universal form of thermodynamic uncertainty relation for Langevin dynamics

The thermodynamic uncertainty relation (TUR) provides a stricter bound for entropy production (EP) than that of the thermodynamic second law. This stricter bound can be utilized to infer the EP and derive other tradeoff relations. Though the validity of the TUR has been verified in various stochastic systems, its application to general Langevin dynamics has not been successfully unified, especially for underdamped Langevin dynamics, where odd parity variables in time-reversal operation such as velocity get involved. Previous TURs for underdamped Langevin dynamics are neither experimentally accessible nor reduced to the original form of the overdamped Langevin dynamics in the zero-mass limit. Here, we find a TUR for underdamped Langevin dynamics with an arbitrary time-dependent protocol, which is operationally accessible when all mechanical forces are controllable. We show that the original TUR is a consequence of our underdamped TUR in the zero-mass limit. This indicates that the TUR formulation presented here can be regarded as the universal form of the TUR for general Langevin dynamics.

Designing circle swimmers: Principles and strategies

Various microswimmers move along circles rather than straight lines due to their swimming mechanisms, body shapes, or hydrodynamic effects. In this paper, we adopt the concepts of stochastic thermodynamics to analyze circle swimmers confined to a two-dimensional plane and study the trade-off relations between various physical quantities, such as precision, energy cost, and rotational speed. Based on these findings, we predict principles and strategies for designing microswimmers of special optimized functions under limited energy resource conditions, which will bring new experimental inspiration for designing smart motors.

Modeling of biomolecular machines in non-equilibrium steady states

Numerical computations have become a pillar of all modern quantitative sciences. Any computation involves modeling-even if often this step is not made explicit-and any model has to neglect details while still being physically accurate. Equilibrium statistical mechanics guides both the development of models and numerical methods for dynamics obeying detailed balance. For systems driven away from thermal equilibrium, such a universal theoretical framework is missing. For a restricted class of driven systems governed by Markov dynamics and local detailed balance, stochastic thermodynamics has evolved to fill this gap and to provide fundamental constraints and guiding principles. The next step is to advance stochastic thermodynamics from simple model systems to complex systems with tens of thousands or even millions of degrees of freedom. Biomolecules operating in the presence of chemical gradients and mechanical forces are a prime example for this challenge. In this Perspective, we give an introduction to isothermal stochastic thermodynamics geared toward the systematic multiscale modeling of the conformational dynamics of biomolecular and synthetic machines, and we outline some of the open challenges.

Irreversibility, Loschmidt Echo, and Thermodynamic Uncertainty Relation

Entropy production characterizes irreversibility. This viewpoint allows us to consider the thermodynamic uncertainty relation, which states that a higher precision can be achieved at the cost of higher entropy production, as a relation between precision and irreversibility. Considering the original and perturbed dynamics, we show that the precision of an arbitrary counting observable in continuous measurement of quantum Markov processes is bounded from below by the Loschmidt echo between the two dynamics, representing the irreversibility of quantum dynamics. When considering particular perturbed dynamics, our relation leads to several thermodynamic uncertainty relations, indicating that our relation provides a unified perspective on classical and quantum thermodynamic uncertainty relations.

Detailed fluctuation theorem bound for apparent violations of the second law

The second law of thermodynamics is a statement about the statistics of the entropy production, 〈Σ〉≥0. For small systems, it is known that the entropy production is a random variable and negative values (Σ<0) might be observed in some experiments. This situation is sometimes called apparent violation of the second law. In this sense, how often is the second law violated? For a given average 〈Σ〉, we show that the strong detailed fluctuation theorem implies a lower tight bound for the apparent violations of the second law. As applications, we verify that the bound is satisfied for the entropy produced in the heat exchange problem between two reservoirs mediated by a bosonic mode in the weak-coupling approximation, a levitated nanoparticle, and a classical particle in a box.

Cycle counts and affinities in stochastic models of nonequilibrium systems

For nonequilibrium systems described by finite Markov processes, we consider the number of times that a system traverses a cyclic sequence of states (a cycle). The joint distribution of the number of forward and backward instances of any given cycle is described by universal formulas which depend on the cycle affinity, but are otherwise independent of system details. We discuss the similarities and differences of this result to fluctuation theorems, and generalize the result to families of cycles, relevant under coarse graining. Finally, we describe the application of large deviation theory to this cycle-counting problem.

Current fluctuations in nonequilibrium discontinuous phase transitions

Discontinuous phase transitions out of equilibrium can be characterized by the behavior of macroscopic stochastic currents. But while much is known about the average current, the situation is much less understood for higher statistics. In this paper, we address the consequences of the diverging metastability lifetime-a hallmark of discontinuous transitions-in the fluctuations of arbitrary thermodynamic currents, including the entropy production. In particular, we center our discussion on the conditional statistics, given which phase the system is in. We highlight the interplay between integration window and metastability lifetime, which is not manifested in the average current, but strongly influences the fluctuations. We introduce conditional currents and find, among other predictions, their connection to average and scaled variance through a finite-time version of large deviation theory and a minimal model. Our results are then further verified in two paradigmatic models of discontinuous transitions: Schlögl's model of chemical reactions, and a 12-state Potts model subject to two baths at different temperatures.

Thermodynamic uncertainty relations for many-body systems with fast jump rates and large occupancies

A universal large N theory of nonequilibrium fluctuations emerges in the limit of fast jump rates and large occupancies. We use this theory to derive a set of coarse-grained thermodynamic uncertainty relations-one of them being an activity bound. Importantly, the activity serves as a tighter bound for the entropy production in 1D systems. These results are particularly useful in the many-body regime, where typically a coarse-grained approach is required to handle the large microscopic state space.

Higher-order efficiency bound and its application to nonlinear nanothermoelectrics

Power and efficiency of heat engines are two conflicting objectives. A tight efficiency bound is expected to give insights on the fundamental properties of such a power-efficiency tradeoff. Here, we derive an upper bound on the efficiency of steady-state heat engines, which incorporates higher-order fluctuations of power. In a prototypical model of nonlinear nanostructured thermoelectrics, we show that the obtained bound is tighter than a well-established efficiency bound derived from the thermodynamic uncertainty relation, demonstrating that the higher-order terms have rich information about the thermodynamic efficiency in the nonlinear regime. In particular, we find that the higher-order bound is exactly achieved if the tight coupling condition is satisfied. The obtained bound gives a consistent prediction with an observation that nonlinearity enhances the power-efficiency tradeoff, and would also be useful in a variety of nanoscale engines.

Exploiting the fundamentals of biological organization for the advancement of biofabrication

The field of biofabrication continues to progress, offering higher levels of spatial control, reproducibility, and functionality. However, we remain far from recapitulating what nature has achieved. Biological systems such as tissues and organs are assembled from the bottom-up through coordinated supramolecular and cellular processes that result in their remarkable structures and functionalities. In this perspective, we propose that incorporating such biological assembling mechanisms within fabrication techniques, offers an opportunity to push the boundaries of biofabrication. We dissect these mechanisms into distinct biological organization principles (BOPs) including self-assembly, compartmentalization, diffusion-reaction, disorder-to-order transitions, and out-of-equilibrium processes. We highlight recent work demonstrating the viability and potential of these approaches to enhance scalability, reproducibility, vascularization, and biomimicry; as well as current challenges to overcome.

Algorithmic Approaches for Assessing Irreversibility in Time Series: Review and Comparison

The assessment of time irreversibility, i.e., of the lack of invariance of the statistical properties of a system under the operation of time reversal, is a topic steadily gaining attention within the research community. Irreversible dynamics have been found in many real-world systems, with alterations being connected to, for instance, pathologies in the human brain, heart and gait, or to inefficiencies in financial markets. Assessing irreversibility in time series is not an easy task, due to its many aetiologies and to the different ways it manifests in data. It is thus not surprising that several numerical methods have been proposed in the last decades, based on different principles and with different applications in mind. In this contribution we review the most important algorithmic solutions that have been proposed to test the irreversibility of time series, their underlying hypotheses, computational and practical limitations, and their comparative performance. We further provide an open-source software library that includes all tests here considered. As a final point, we show that "one size does not fit all", as tests yield complementary, and sometimes conflicting views to the problem; and discuss some future research avenues.

Superconducting-like Heat Current: Effective Cancellation of Current-Dissipation Trade-Off by Quantum Coherence

Quantum coherence is a useful resource for increasing the speed and decreasing the irreversibility of quantum dynamics. Because of this feature, coherence is used to enhance the performance of various quantum information processing devices beyond the limitations set by classical mechanics. However, when we consider thermodynamic processes, such as energy conversion in nanoscale devices, it is still unclear whether coherence provides similar advantages. Here we establish a universal framework, clarifying how coherence affects the speed and irreversibility in thermodynamic processes described by the Lindblad master equation, and give general rules for when coherence enhances or reduces the performance of thermodynamic devices. Our results show that a proper use of coherence enhances the heat current without increasing dissipation; i.e., coherence can reduce friction. In particular, if the amount of coherence is large enough, this friction becomes virtually zero, realizing a superconducting-like "dissipation-less" heat current. Since our framework clarifies a general relation among coherence, energy flow, and dissipation, it can be applied to many branches of science from quantum information theory to biology. As an application to energy science, we construct a quantum heat engine cycle that exceeds the power-efficiency trade-off bound on classical engines and effectively attains the Carnot efficiency with finite power in fast cycles.

Lower Bound on Irreversibility in Thermal Relaxation of Open Quantum Systems

We consider the thermal relaxation process of a quantum system attached to single or multiple reservoirs. Quantifying the degree of irreversibility by entropy production, we prove that the irreversibility of the thermal relaxation is lower bounded by a relative entropy between the unitarily evolved state and the final state. The bound characterizes the state discrepancy induced by the nonunitary dynamics, and thus reflects the dissipative nature of irreversibility. Intriguingly, the bound can be evaluated solely in terms of the initial and final states and the system Hamiltonian, thereby providing a feasible way to estimate entropy production without prior knowledge of the underlying coupling structure. This finding refines the second law of thermodynamics and reveals a universal feature of thermal relaxation processes.

Universal Bounds on Fluctuations in Continuous Thermal Machines

We study bounds on ratios of fluctuations in steady-state time-reversal energy conversion devices. In the linear response regime, we prove that the relative fluctuations (precision) of the output current (power) is always lower bounded by the relative fluctuations of the input current (heat current absorbed from the hot bath). As a consequence, the ratio between the fluctuations of the output and input currents are bounded both from above and below, where the lower (upper) bound is determined by the square of the averaged efficiency (square of the Carnot efficiency) of the engine. The saturation of the lower bound is achieved in the tight-coupling limit when the determinant of the Onsager response matrix vanishes. Our analysis can be applied to different operational regimes, including engines, refrigerators, and heat pumps. We illustrate our findings in two types of continuous engines: two-terminal coherent thermoelectric junctions and three-terminal quantum absorption refrigerators. Numerical simulations in the far-from-equilibrium regime suggest that these bounds apply more broadly, beyond linear response.

Thermodynamic Uncertainty Relation and Thermodynamic Speed Limit in Deterministic Chemical Reaction Networks

We generalize the thermodynamic uncertainty relation (TUR) and thermodynamic speed limit (TSL) for deterministic chemical reaction networks (CRNs). The scaled diffusion coefficient derived by considering the connection between macro- and mesoscopic CRNs plays an essential role in our results. The TUR shows that the product of the entropy production rate and the ratio of the scaled diffusion coefficient to the square of the rate of concentration change is bounded below by two. The TSL states a trade-off relation between speed and thermodynamic quantities, the entropy production, and the time-averaged scaled diffusion coefficient. The results are proved under the general setting of open and nonideal CRNs.

A strong nonequilibrium bound for sorting of cross-linkers on growing biopolymers

Understanding the role of nonequilibrium driving in self-organization is crucial for developing a predictive description of biological systems, yet it is impeded by their complexity. The actin cytoskeleton serves as a paradigm for how equilibrium and nonequilibrium forces combine to give rise to self-organization. Motivated by recent experiments that show that actin filament growth rates can tune the morphology of a growing actin bundle cross-linked by two competing types of actin-binding proteins [S. L. Freedman et al., Proc. Natl. Acad. Sci. U.S.A. 116, 16192-16197 (2019)], we construct a minimal model for such a system and show that the dynamics of a growing actin bundle are subject to a set of thermodynamic constraints that relate its nonequilibrium driving, morphology, and molecular fluxes. The thermodynamic constraints reveal the importance of correlations between these molecular fluxes and offer a route to estimating microscopic driving forces from microscopy experiments.

Improved bound on entropy production in a quantum annealer

For a system described by a multivariate probability density function obeying the fluctuation theorem, the average dissipation is lower bounded by the degree of asymmetry of the marginal distributions (namely the relative entropy between the marginal and its mirror image). We formally prove that such a lower bound is tighter than the recently reported bound expressed in terms of the precision of the marginal (i.e., the thermodynamic uncertainty relation) and is saturable. We illustrate the result with examples and we apply it to achieve one of the most accurate experimental estimations of dissipation associated with quantum annealing to date.

Heat fluctuations in a harmonic chain of active particles

One of the major challenges in stochastic thermodynamics is to compute the distributions of stochastic observables for small-scale systems for which fluctuations play a significant role. Hitherto much theoretical and experimental research has focused on systems composed of passive Brownian particles. In this paper, we study the heat fluctuations in a system of interacting active particles. Specifically we consider a one-dimensional harmonic chain of N active Ornstein-Uhlenbeck particles, with the chain ends connected to heat baths of different temperatures. We compute the moment-generating function for the heat flow in the steady state. We employ our general framework to explicitly compute the moment-generating function for two example single-particle systems. Further, we analytically obtain the scaled cumulants for the heat flow for the chain. Numerical Langevin simulations confirm the long-time analytical expressions for first and second cumulants for the heat flow for a two-particle chain.

The Problem of Engines in Statistical Physics

Engines are open systems that can generate work cyclically at the expense of an external disequilibrium. They are ubiquitous in nature and technology, but the course of mathematical physics over the last 300 years has tended to make their dynamics in time a theoretical blind spot. This has hampered the usefulness of statistical mechanics applied to active systems, including living matter. We argue that recent advances in the theory of open quantum systems, coupled with renewed interest in understanding how active forces result from positive feedback between different macroscopic degrees of freedom in the presence of dissipation, point to a more realistic description of autonomous engines. We propose a general conceptualization of an engine that helps clarify the distinction between its heat and work outputs. Based on this, we show how the external loading force and the thermal noise may be incorporated into the relevant equations of motion. This modifies the usual Fokker-Planck and Langevin equations, offering a thermodynamically complete formulation of the irreversible dynamics of simple oscillating and rotating engines.

Violating the thermodynamic uncertainty relation in the three-level maser

Nanoscale heat engines are subject to large fluctuations which affect their precision. The thermodynamic uncertainty relation (TUR) provides a trade-off between output power, fluctuations, and entropic cost. This trade-off may be overcome by systems exhibiting quantum coherence. This Letter provides a study of the TUR in a prototypical quantum heat engine, the Scovil-Schulz-DuBois maser. Comparison with a classical reference system allows us to determine the effect of quantum coherence on the performance of the heat engine. We identify analytically regions where coherence suppresses fluctuations, implying a quantum advantage, as well as regions where fluctuations are enhanced by coherence. This quantum effect cannot be anticipated from the off-diagonal elements of the density matrix. Because the fluctuations are not encoded in the steady state alone, TUR violations are a consequence of coherence that goes beyond steady-state coherence. While the system violates the conventional TUR, it adheres to a recent formulation of a quantum TUR. We further show that parameters where the engine operates close to the conventional limit are prevalent and TUR violations in the quantum model are not uncommon.

Thermodynamic Uncertainty Relation Bounds the Extent of Anomalous Diffusion

In a finite system driven out of equilibrium by a constant external force the thermodynamic uncertainty relation (TUR) bounds the variance of the conjugate current variable by the thermodynamic cost of maintaining the nonequilibrium stationary state. Here we highlight a new facet of the TUR by showing that it also bounds the timescale on which a finite system can exhibit anomalous kinetics. In particular, we demonstrate that the TUR bounds subdiffusion in a single file confined to a ring as well as a dragged Gaussian polymer chain even when detailed balance is satisfied. Conversely, the TUR bounds the onset of superdiffusion in the active comb model. Remarkably, the fluctuations in a comb model evolving from a steady state behave anomalously as soon as detailed balance is broken. Our work establishes a link between stochastic thermodynamics and the field of anomalous dynamics that will fertilize further investigations of thermodynamic consistency of anomalous diffusion models.

Cost-precision trade-off relation determines the optimal morphogen gradient for accurate biological pattern formation

Spatial boundaries formed during animal development originate from the pre-patterning of tissues by signaling molecules, called morphogens. The accuracy of boundary location is limited by the fluctuations of morphogen concentration that thresholds the expression level of target gene. Producing more morphogen molecules, which gives rise to smaller relative fluctuations, would better serve to shape more precise target boundaries; however, it incurs more thermodynamic cost. In the classical diffusion-depletion model of morphogen profile formation, the morphogen molecules synthesized from a local source display an exponentially decaying concentration profile with a characteristic length λ. Our theory suggests that in order to attain a precise profile with the minimal cost, λ should be roughly half the distance to the target boundary position from the source. Remarkably, we find that the profiles of morphogens that pattern the Drosophila embryo and wing imaginal disk are formed with nearly optimal λ. Our finding underscores the cost-effectiveness of precise morphogen profile formation in Drosophila development.

Dismantling Anti-Ageing Medicine: Why Age-Relatedness of Cardiovascular Disease is Proof of Robustness Rather Than of Ageing-Associated Vulnerability

Ageing is perceived to be the common culprit behind the most prevalent noncommunicable chronic diseases (NCD) such as cardiovascular disease (CVD). Treating ageing as a means to prevent its downstream pathologies has become the logical extension of this idea, and the defining criterion of anti-ageing medicine (evidence-based early detection, prevention, and treatment of age-related diseases). Challenging the underlying rationale, we here argue that the disease's late-in-life occurrence is proof of a genetically conserved robustness that helps us resist disease long enough for it to masquerade as a consequence of living long rather than of living wrong. Robustness is an acknowledged hallmark phenomenon of all complex systems (while there exists no universally adopted definition, a hallmark of complex systems is that they consist of many networked components whose interactions may give rise to system behaviors which cannot be derived or predicted from a reductionist knowledge of the interacting parts, even if this knowledge is complete) and a key concept in the complexity sciences (a relatively new branch of science that attempts to find and understand the common mechanisms and patterns shared by all complex systems). To reconceptualise the age-relatedness of chronic diseases in this sense has important implications for medical research and practice. The goal of our essay is to open a discussion that may enhance the overall understanding of robustness and prevent a misguided redirection of funding away from established disease specific research and towards anti-ageing medicine. This essay is timely, as the forthcoming 11^th version of the International Classification of Diseases (ICD) will be the first to recognise ageing as a condition, thereby legitimising anti-ageing medical research. On a more pragmatic note, and for the benefit of people alive today, we propose a practical strategy to remedy the mismatch between heritable robustness and the lifestyle challenges that gradually overwhelm it.

Bounds on fluctuations for finite-time quantum Otto cycle

For quantum Otto engine driven quasistatically, we provide exact full statistics of heat and work for a class of working fluids that follow a scale-invariant energy eigenspectra under driving. Equipped with the full statistics we go on to derive a universal expression for the ratio of nth cumulant of output work and input heat in terms of the mean Otto efficiency. Furthermore, for nonadiabatic driving of quantum Otto engine with working fluid consisting of either a (i) qubit or (ii) a harmonic oscillator, we show that the relative fluctuation of output work is always greater than the corresponding relative fluctuation of input heat absorbed from the hot bath. As a result, the ratio between the work fluctuation and the input heat fluctuation receives a lower bound in terms of the square value of the average efficiency of the engine. The saturation of the lower bound is received in the quasistatic limit of the engine.

Kinetic uncertainty relation on first-passage time for accumulated current

The kinetic uncertainty relation (KUR) is a trade-off relation between the precision of an observable and the mean dynamical activity in a fixed time interval for a time-homogeneous and continuous-time Markov chain. In this Letter, we derive the KUR on the first passage time for the time-integrated current from the information inequality at stopping times. The relation shows that the precision of the first passage time is bounded from above by the mean number of jumps up to that time. We apply our result to simple systems and demonstrate that the activity constraint gives a tighter bound than the thermodynamic uncertainty relation in the regime far from equilibrium.

Physical bioenergetics: Energy fluxes, budgets, and constraints in cells

Cells are the basic units of all living matter which harness the flow of energy to drive the processes of life. While the biochemical networks involved in energy transduction are well-characterized, the energetic costs and constraints for specific cellular processes remain largely unknown. In particular, what are the energy budgets of cells? What are the constraints and limits energy flows impose on cellular processes? Do cells operate near these limits, and if so how do energetic constraints impact cellular functions? Physics has provided many tools to study nonequilibrium systems and to define physical limits, but applying these tools to cell biology remains a challenge. Physical bioenergetics, which resides at the interface of nonequilibrium physics, energy metabolism, and cell biology, seeks to understand how much energy cells are using, how they partition this energy between different cellular processes, and the associated energetic constraints. Here we review recent advances and discuss open questions and challenges in physical bioenergetics.

Thermodynamic Optimality of Glycolytic Oscillations

Temporal order in living matters reflects the self-organizing nature of dynamical processes driven out of thermodynamic equilibrium. Because of functional reasons, the period of a biochemical oscillation must be tuned to a specific value with precision; however, according to the thermodynamic uncertainty relation (TUR), the precision of the oscillatory period is constrained by the thermodynamic cost of generating it. After reviewing the basics of chemical oscillations using the Brusselator as a model system, we study the glycolytic oscillation generated by octameric phosphofructokinase (PFK), which is known to display a period of several minutes. By exploring the phase space of glycolytic oscillations, we find that the glycolytic oscillation under the cellular condition is realized in a cost-effective manner. Specifically, over the biologically relevant range of parameter values of glycolysis and octameric PFK, the entropy production from the glycolytic oscillation is minimal when the oscillation period is (5-10) min. Furthermore, the glycolytic oscillation is found at work near the phase boundary of limit cycles, suggesting that a moderate increase of glucose injection rate leads to the loss of oscillatory dynamics, which is reminiscent of the loss of pulsatile insulin release resulting from elevated blood glucose level.