Stochastic Thermodynamics: Experiment and Theory

Biology is intrinsically noisy at all levels, from molecules to cells, tissues, organs, communities and ecosystems. While thermodynamic processes in ordinary matter are driven by free-energy minimization, living matter and biology delineate a fascinating nonequilibrium state predominantly governed by information flows through all organizational levels. Whereas we know how to measure energy and entropy in physical systems we have poor knowledge about measuring information-content in general. Recent developments in the fields of stochastic thermodynamics and thermodynamic-information feedback combined with single molecule experiments show the way to define information-content in nonequilibrium systems. In this talk I will describe how to measure information-content in two classes of nonequilibrium systems. First, I will introduce the Continuous Maxwell Demon, a new paradigm of information-to-energy conversion, and demonstrate how work extraction beats the Landauer limit without violating the second law. Next, I will demonstrate the validity of a fluctuation theorem in nonequilibrium systems under continuous-time feedback and show how to measure information-content in such conditions. Second, I will introduce a mutational ensemble of DNA hairpin folders and show how to measure information-content in this context. A definition of information-content applicable to generic disordered populations is proposed. All results are tested in single molecule pulling experiments.

This talk will be focus on the question of the physical contents of the Gibbs-Shannon entropy outside equilibrium. Article : Gavrilov-Chetrite-Bechhoeffer : Direct measurement of weakly nonequilibrium system entropy is consistent with Gibbs-Shannon form. PNAS 2017.

Equipartition principle plays a central role in the understanding of the physics of systems in equilibrium: the mean potential and kinetic energy of each degree of freedom equilibrates to $k_BT/2$, with $k_B$ the Boltzmann constant and $T$ the temperature. This equality is linked to the fluctuation-dissipation theorem (FDT): fluctuations of one observable are proportional to the temperature and dissipation in the response function associated to that observable. In non equilibrium situations however, such relations between fluctuations and response are not granted, and excess noise is usually expected to be observed with respect to an equilibrium state [1]. In this presentation, we show that the opposite phenomenon can also be experimentally observed: a system that fluctuates less than what would be expected from equilibrium ! Indeed, when we measure the thermal noise of the deflexion of a micro-cantilever subject to a strong stationary temperature gradient (and thus heat flow), fluctuations are much smaller that those expected from the system mean temperature. We will first present the experimental system, an atomic force microscope (AFM) micro-cantilever in vacuum heated at its free extremity with a laser. We will show that this system is small enough to have discrete degrees of freedom but large enough to be in a non-equilibrium steady state (NESS). We will then estimate its temperature profile with the mechanical response of the system [2], and observe that equipartition theorem can not be applied for this NESS: the thermal noise of the system is roughly unchanged while its temperature rises by several hundred degrees ! We will explain how a generalized FDT taking into account the temperature field can account for these observations, if dissipation is not uniform. Further experimental evidences of the validity of this framework will conclude the presentation [3]. We acknowledge the support of ERC project OutEFLUCOP and ANR project HiResAFM. [1] L. Conti, P. D. Gregorio, G. Karapetyan, C. Lazzaro, M. Pegoraro, M. Bonaldi, and L. Rondoni, Effects of breaking vibrational energy equipartition on measurements of temperature in macroscopic oscillators subject to heat flux, J. Stat. Mech. P12003 (2013) [2] F. Aguilar, M. Geitner, E. Bertin and L. Bellon, Resonance frequency shift of strongly heated micro-cantilevers, Journal of Applied Physics 117, 234503 (2015) [3] M. Geitner, F. Aguilar, E. Bertin and L. Bellon, Low thermal fluctuations in a system heated out of equilibrium, Physical Review E 95, 032138 (2017)

Gravitational wave interferometers have recently made the first detections, opening the era of gravitational-wave and multi-messenger astronomy. In the coming years both LIGO and Virgo will undergo a planned series of experimental upgrades to further increase the sensitivity; moreover a completely new generation of instruments is being studied with the aim of increasing the astrophysical reach by at least a factor 10, while also extending the bandwidth towards lower frequencies. In both cases, the design choices depend critically on the full control of the noise budget: this is a rather complex task due to the level of sophistication of these macroscopic instruments which are designed to be limited by a combination of few fundamental noise sources. Together with quantum noise and local gravity gradients, thermal noise is expected to be a dominating contribution to the instrument ultimate noise. Its contribution is traditionally estimated under the hypothesis of thermal equilibrium, in spite of the thermal gradients and heat fluxes that are present in the instruments' key components. While the deviation may be modest in current detectors, futures designs relying on cryogenic operation foresee much more extreme non-equilibrium conditions that can severely compromise the applicability of predictions made assuming equilibrium. The reason for the widespread and often improper assumption of equilibrium is that, for solids, a viable theory that describes thermal noise away from thermodynamic equilibrium does not exist yet. Experimental data is scarce, but does suggest the possibility, in some cases, of a substantial enhancement of spontaneous fluctuations compared to the equilibrium condition, similarly to what is observed in fluids. I will discuss the design of gravitational wave interferometers focusing on nonequilibrium driving cases and will present experimental data on the spontaneous fluctuations of solids in nonequilibrium steady states.

Stochastic thermodynamics provides a useful set of tools to analyze and constrain the behavior of far from equilibrium systems. In this talk, we will report an application of ideas from stochastic thermodynamics to the problem of membrane growth. Non-equilibrium forcing of the membrane can cause it to buckle and undergo a morphological transformation. We show how ideas from stochastic thermodynamics, in particular, a recent application to self-assembly, can be used to phenomenologically describe and constrain morphological changes excited during a non-equilibrium growth process.

Stochastic thermodynamics provides a framework to describe small driven systems using thermodynamic notions. Since the conceptual basis is now firmly established, the challenge is to explore whether and how these concepts can be used to infer otherwise hidden properties of systems. After recalling the foundations, I will report on our recent progress following this strategy. In particular, I will elucidate the form of entropy production in active systems and derive model-independent bounds on the efficiency of molecular motors and small heat engines. For the latter, I will resolve the recent debate whether or not Carnot efficiency can be reached at finite power.

We study the diffusive dynamics of a Brownian particle in the proximity of a flat surface under nonequilibrium conditions, which are created by an anisotropic thermal environment with different temperatures being active along distinct spatial directions. By presenting the exact time-dependent solution of the Fokker-Planck equation for this problem, we demonstrate that the interplay between anisotropic diffusion and hard-core interaction with the plain wall rectifies the thermal fluctuations and induces directed particle transport parallel to the surface, without any deterministic forces being applied in that direction. Based on current micromanipulation technologies, we suggest a concrete experimental setup to observe this novel noise-induced transport mechanism. We furthermore show that it is sensitive to particle characteristics, such that this setup can be used for sorting particles of different sizes.

The response of thermodynamic systems perturbed out of an equilibrium steady-state is described by the reciprocal and the fluctuation-dissipation relations. The so-called fluctuation theorems extended the study of fluctuations far beyond equilibrium. All these results rely on the crucial assumption that the observer has complete information about the system. Such a precise control is difficult to attain, hence the following questions are compelling: Will an observer who has marginal information be able to perform an effective thermodynamic analysis? Given that such observer will only establish local equilibrium amidst the whirling of hidden degrees of freedom, by perturbing the stalling currents will he/she observe equilibrium-like fluctuations? We model the dynamics of open systems as Markov jump processes on finite networks. We establish that: 1) While marginal currents do not obey a full-fledged fluctuation relation, there exist effective affinities for which an integral fluctuation relation holds; 2) Under reasonable assumptions on the parametrization of the rates, effective and "real" affinities only differ by a constant; 3) At stalling, i.e. where the marginal currents vanish, a symmetrized fluctuation-dissipation relation holds while reciprocity does not; 4) There exists a notion of marginal time-reversal that plays a role akin to that played by time-reversal for complete systems, which restores the fluctuation relation and reciprocity. The above results hold for configuration-space currents, and for phenomenological currents provided that certain symmetries of the effective affinities are respected - a condition whose range of validity we deem the most interesting question left open to future inquiry. Our results are constructive and operational: we provide an explicit expression for the effective affinities and propose a procedure to measure them in laboratory.

Superconducting circuits provide a platform for stochastic thermodynamics experiments in both classical and quantum regimes (“circuit Quantum Thermodynamics”). I first review the ideas, principles and examples of classical experiments utilizing single electron charge as the stochastic variable. I present experiments over the past several years on classical fluctuation relations and Maxwell Demons (MD), the latter in form of both non-autonomous Szilard Engines and autonomous MDs. Recent highlights on entropy reduction and rare events will be reviewed. In the second part of the talk I focus on open quantum systems formed of superconducting qubits and resonators, coupled to heat baths. In this context microwave photons carry the heat between the system and bath. I present experiments on quantum heat transport mediated by a transmon qubit, progress on superconducting quantum heat engines and refrigerators, and on detecting single microwave photon quanta. Success in the last item would allow us to perform true stochastic thermodynamics experiments in the quantum regime, and to realize quantum MDs.

Essential to any well-functioning thermodynamic engine is the rapid and reliable extraction of work at high thermodynamic efficiency. Accomplishing this goal requires not only quantifying the trade-offs between power and efficiency, but also doing so while constraining power fluctuations. Whereas the thermodynamic uncertainty relation offers universal constraints on power fluctuations for autonomous steady state heat engines, no such statement can be made about cyclically-operating nonautonomous engines. As a first step in this direction, I will characterize in this talk those optimal finite-time thermodynamic protocols that optimize the compromise between work and work fluctuations for two canonical models of driven mesoscopic systems – a harmonically-trapped Brownian particle and a quantum dot. Remarkably, we find that as we shift the weight of our optimization objective from average work to work standard deviation, there is an analog of a first-order phase transition in protocol space: two distinct protocols exchange global optimality with mixed protocols akin to phase coexistence.

In this decade, thermodynamics of information has attracted much attention both theoretically and experimentally [1]. Maxwell's demon plays a significant role, which is regarded as a feedback controller acting on stochastic thermodynamic systems. In this talk, I will discuss a theory of Maxwell's demons with autonomous measurement and feedback control that are performed continuously in time. Especially, I will focus on the generalized second law and fluctuation theorem [2], by incorporating continuous information flow (or the learning rate). I will also show that the Onsager reciprocity holds true in the presence of unconventional thermodynamic force called information affinity [3]. [1] J. M. R. Parrondo, J. M. Horowitz, T. Sagawa, Nature Physics 11, 131-139 (2015). [2] N. Shiraishi, T. Sagawa, Phys. Rev. E E 91, 012130 (2015). [3] S. Yamamoto, S. Ito, N. Shiraishi, T. Sagawa, Phys. Rev. E 94, 052121 (2016).

So-called "violations" of the second law are a fascinating feature of the thermodynamics of nanoscale systems. When a macroscopic system undergoes an isothermal process, the second law of thermodynamics is given by the inequality W >= Delta F, which states that the work performed on the system must be no less than the free energy difference between initial and final states. For nanoscale systems, one can observe occasional violations of this inequality. A natural measure of the magnitude of the violation is given by the dimensionless quantity x = (Delta F - W)/kT. I will derive a simple expression that provides a bound on the probability of observing such violations, as a function of x, and I will argue that this expression provides the tightest possible universal bound. I will also discuss a simple model system for which this bound can be saturated, and will argue that this model is experimentally realizable using quantum dots. Along the way, I will describe a model process for which nearly every realization results in a "violation" of the second law, i.e. W < Delta F almost always, but on average the second law remains valid: > Delta F, where the angular brackets denote an average over infinitely many realizations.

I will review our past work on the quantitative connection between entropy production and irreversibility, as measured by the relative entropy between forward and backward trajectories. In the last part of the talk, I will present some recent work on the application of those ideas to semi-Markov chains, which are relevant to estimate entropy production in molecular motors and kinetic networks when the observer has only access to a restricted number of variables.

Experimental detection of non-vanishing probability currents in biophysical dynamical systems has been utilized to classify process as being in or out of equilibrium. It has been proposed that the thermodynamic uncertainty relation (TUR) provides a route to a more quantitative analysis, allowing one to infer a bound on the mean dissipation rate based fluctuations in the probability currents. Using a standard model consisting of harmonic springs connecting beads at different temperatures, we investigate various strategies for dissipation estimation from fluctuating currents. We explore the tightness of the TUR inequality and the convergence rate of the estimators.

We calculate the large deviation function of the end-to-end distance and the corresponding extension-versus-force relation for random walks. For off-lattice random walks with persistence in higher dimensions, the large-deviation function undergoes a first order phase transition. In 4 dimensions the system is perfectly harmonic.

It recently appeared that a dissipative steady state energy reservoir behaves similarly, in many ways, as the equilibrium thermostat usually considered in statistical physics. One of our objectives is to study experimentally to what extent this analogy persists. Recent results on granular gas systems will be presented.

Statistical mechanics gets very relevant to cosmology when fluctuations are being studied. We provide some input into the well-known puzzles and paradoxes known under such names as the horizon paradox, the flatness problem, the information paradox and the dark energy puzzle.

We study the processes in which fluctuating elements of a system are progressively fixed (quenched) while keeping the interaction with the remaining unfixed elements. If the interaction is global among the Ising spin elements and if the unfixed part is re-equilibrated each time after fixing an element, the evolution of large system is martingale about the equilibrium spin value of the unfixed spins. Due to this property the system starting from the critical point yields the final magnetization whose distribution shows non-Gaussian and slow transient scaling with the system.

Systems with long-range interactions have an inter-particle interaction potential that decays slower than $1/r^d$ in $d$ dimensions. Examples are widespread, from plasmas, dipolar ferroelectrics and ferromagnets, to gravitational systems. I will dwell on the question: What happens when a long-range system is driven out of thermal equilibrium by, e.g., an impulsive kick? In similar situations, short-range systems would typically relax to another thermal equilibrium with a uniform temperature across the system. By contrast, a long-range system relaxes to non-Boltzmann nonequilibrium stationary states that support a non-uniform temperature profile across the system. More striking and counterintuitive is the observation of temperature inversion in such states: denser parts of the system are colder than dilute ones. Such inversions occur in nature, e.g., in the solar corona and in interstellar molecular clouds. We demonstrate how an interplay of wave-particle interaction and spatial inhomogeneity offers a simple and appealing mechanism to explain temperature inversion in generic long-range systems.

A key assumption in the thermodynamic description of macroscopic systems is that the system’s interaction with its environment is very small and can be neglected. For microscopic systems, however, this assumption breaks down. In this talk I will discuss the impact of strong coupling between system and its environment on the standard repertoire of thermodynamics and non-equilibrium dynamics. I will begin with the description of out-of-equilibrium dynamics for which we show that the stochastic entropy production of a strongly coupled system satisfies a generalised Crooks relation [2,3], which can be used to quantify time-asymmetry of correlated non-equilibrium processes. I will then discuss our strong coupling version of Bohr’s thermodynamic uncertainty relation [4], which limits the simultaneous sharpness of knowing the temperature and energy of a system in equilibrium. This generalised thermodynamic uncertainty relation is derived using quantum estimation theory and is valid for classical and quantum systems at all coupling strengths [4]. It turns out that in the quantum regime, strong coupling can lead to non-commutativity effects that increase the uncertainty in temperature and modify the heat capacity. Surprisingly, these quantum fluctuations are described by the average Wigner-Yanase-Dyson skew information, a quantity intimately connected to measures of coherence. [1] T. Philbin, J. Anders, J. Phys. A: Math. Theor. 49, 215303 (2016) [2] H. Miller, J. Anders, Phys. Rev. E 95, 062123 (2017) [3] P. Strasberg, M. Esposito, Phys. Rev. E 95, 062101 (2017) [4] H. Miller, J. Anders, arxiv: 1801.08057 (2018) - to appear in Nat. Comm.

Many motile organisms have developed intriguing steering mechanisms allowing them to orientate and navigate within gravitational, chemical or light fields. Such tactic response strongly facilitates e.g., the search for food, reproduction and/or escape from unfavorable ambient conditions and is therefore an essential aspect of life. Unlike living systems (bacteria, motile cells), where tactic behavior is typically achieved by complex internal signal pathways, it is not obvious how this can be realized with synthetic microswimmers, which have much simpler internal structures. Using light-activated self-propelled particles, we demonstrate that autonomous steering in gravitational fields and light gradients can be achieved without invoking a complex internal machinery but simply by the combination of viscous forces and torques, which naturally arise during self-propulsion in liquids. In addition, we demonstrate, how to realize different types of “communication” rules between particles and how this affects, e.g. the cluster formation in such systems. Because the interaction between particles can be easily varied (range of interaction, local vs. non-local interactions), this allows us to study the conditions, under which cooperative phenomena such as cluster and swarm formation can be generated in active systems.

The mechanochemical coupling plays a fundamental role in the thermodynamics of many motors working in fluctuating environments, as well as in the thermodynamics of information processing at the molecular scale. Indeed, it is the coupling between reaction and mechanics that generates the energy transduction powering the motion of these motors. For enzymatic motors such as ATPase or polymerases, the coupling takes place inside the enzyme and its catalytic sites. For active particles such as Janus particles powered by self-diffusiophoresis, propulsion relies on the coupling between the fluid velocity fields and the concentration fields induced by asymmetric catalytic reactions on the motor surface. The consistency with microreversibility implies that a mechanochemical fluctuation theorem should hold for the joint probability of the position of the motor and the number of reactive events. This theorem is obtained starting from the master equation of the underlying stochastic process. For self-phoretic motors, this stochastic process is ruled by coupled Langevin equations for the translational, rotational, and chemical fluctuations. These results predict reciprocal effects between reaction and propulsion that can be tested experimentally. References: [1] P. Gaspard and R. Kapral, Mechanochemical fluctuation theorem and thermodynamics of self-phoretic motors, J. Chem. Phys. 147 (2017) 211101. [2] P. Gaspard and R. Kapral, Fluctuating chemohydrodynamics and the stochastic motion of self-diffusiophoretic particles, J. Chem. Phys. 148 (2018) 134104. [3] P. Gaspard, Kinetic theory and thermodynamics of template-directed copolymerization, J. Stat. Mech. (2017) 024003. [4] P. Gaspard, Kinetic theory and thermodynamics of living copolymerization processes, Phil. Trans. R. Soc. A 374 (2016) 20160147. [5] P. Gaspard, Kinetic theory and thermodynamics of DNA polymerases, Phys. Rev. E 93 (2016) 042419 & 042420.

Feedback control mechanisms are ubiquitous in science and technology. They play an essential role in regulating physical, biological and engineering systems. The standard second law of thermodynamics does not hold in the presence of measurement and feedback. Most studies so far have extended the second law for discrete, Markovian feedback protocols. However, non-Markovian feedback is omnipresent in processes where the control signal is applied with a non-negligible delay. We have experimentally investigated the thermodynamics of continuous, time-delayed feedback cooling using a levitated nanoparticle. We have demonstrated the validity of a generalized second law for the cooling rate and showed that feedback efficiency is enhanced when non-Markovian effects are included.

Stochastic heat engines can be built using colloidal particles trapped using optical tweezers. Here we review recent experimental realizations of microscopic heat engines. We first revisit the theoretical framework of stochastic thermodynamics that allows to describe the fluctuating behavior of the energy fluxes that occur at mesoscopic scales, and then discuss recent implementations of the colloidal equivalents to the macroscopic Stirling, Carnot and steam engines. These small-scale motors exhibit unique features in terms of power and efficiency fluctuations that have no equivalent in the macroscopic world. We also consider a second pathway for work extraction from colloidal engines operating between active bacterial reservoirs at different temperatures, which could significantly boost the performance of passive heat engines at the mesoscale. Finally, we provide some guidance on how the work extracted from colloidal heat engines can be used to generate net particle or energy currents, proposing a new generation of experiments with colloidal systems. Keywords: thermodynamics; fluctuations; miniaturization; heat engines References 1. Martínez, Roldán, Dinis, and Rica, Soft Matter 13, 22 (2017).

Starting from the most general formulation of stochastic thermodynamics—i.e. a thermodynamically consistent nonautonomous stochastic dynamics describing systems in contact with several reservoirs—we define a procedure to identify the conservative and the minimal set of nonconservative contributions in the entropy production. The former is expressed as the difference between changes caused by time-dependent drivings and a generalized potential difference. The latter is a sum over the minimal set of flux-force contributions controlling the dissipative flows across the system. When the system is initially prepared at equilibrium (e.g. by turning off drivings and forces), a finite-time detailed fluctuation theorem holds for the different contributions. Our approach relies on identifying the complete set of conserved quantities and can be viewed as the extension of the theory of generalized Gibbs ensembles to nonequilibrium situations. References: - R. Rao and M. Esposito, "Conservation Laws shape Dissipation", New J. Phys. 20, 023007 (2018) - M. Polettini, G. Bulnes Cuetara and M. Esposito, "Conservation laws and symmetries in stochastic thermodynamics", Phys. Rev. E 94, 052117 (2016)

Cells must operate far from equilibrium, utilizing and dissipating energy continuously to maintain their organization and to avoid stasis and death. However, they must also avoid unnecessary waste of energy. Recent studies have revealed that molecular machines are extremely efficient thermodynamically when compared to their macroscopic counterparts. However, the principles governing the efficient out-of-equilibrium operation of molecular machines remain a mystery. A theoretical framework has been recently formulated in which a generalized friction coefficient quantifies the energetic efficiency in non-equilibrium processes. Moreover, it posits that to minimize energy dissipation, external control should drive the system along the reaction coordinate with a speed inversely proportional to the square root of that friction coefficient. Here, we demonstrate the utility of this theory for designing and understanding energetically efficient non-equilibrium processes through the unfolding and folding of single DNA hairpins.

Levitated nanoparticles in high vacuum have emerged as a rich playground for exploring different frontiers of physics, particularly on stochastic thermodynamics and the applicability of quantum mechanics at the mesoscale [1-5]. Here, we present recent progress on the implementation of different levitation schemes, allowing for exquisite control over the dynamics of a nanoparticle. In particular, we first report on the precise control of the nonlinear and stochastic bistable dynamics of a levitated nanoparticle in high vacuum. We demonstrate how it can lead to efficient signal amplification schemes, including stochastic resonance [6]. Further, we describe our progress towards the control of nanoparticles with internal degrees of freedom (nanodiamonds with NV centers) by means of a RF ion trap [7,8].Finally, we discuss prospects for experimentation on the low-friction regime of stochastic thermodynamics. [1] J. Gieseler et al. Phys. Rev. Lett. 109, 103603 (2012). [2] J. Gieseler et al. Nature Nano. 9, 358-364 (2014). [3] V. Jain et al. Phys. Rev. Lett. 116, 243601 (2016). [4] N. Kiesel et al. PNAS 110, 14180-14185 (2013). [5] L. Rondin et al. Nature Nanotechnology 12, 1130 (2017). [6] F. Ricci et al. Nature Comms. 8, 15141 (2017). [7] I. Alda et al. Appl. Phys. Lett. 109, 163105 (2016). [8] G.P. Conangla et al. preprint arXiv:1803.05527

A molecular motor is a nano-sized chemical engine that converts chemical free energy to mechanical motions. Hence, the energetics is as important as kinetics in order to understand its operation principle. We present experiments to evaluate the thermodynamic properties of a rotational F1-ATPase motor (F1-motor) at a single-molecule level. We show that the F1-motor achieves 100% thermodynamic efficiency at the stalled state. Furthermore, the motor reduces the internal irreversible heat inside the motor to almost zero and achieves a highly-efficient free energy transduction close to 100% during rotations far from a quasistatic process. We discuss the mechanism of how the F1-motor achieves such a high efficiency, which highlights the remarkable property of the nano-sized engine F1-motor. We also will introduce our challenge to realize artificial molecular motor.

Kinetic theory and thermodynamics of reaction networks are extended to the out-of-equilibrium dynamics of continuous-flow stirred tank reactors (CSTR) and serial transfers. On the basis of their stoichiometry matrix, the conservation laws and the cycles of the network are determined for both dynamics. It is shown that the CSTR and serial transfer dynamics are equivalent in the limit where the time interval between the transfers tends to zero proportionally to the ratio of the fractions of fresh to transferred solutions. These results are illustrated with a finite cross-catalytic reaction network and an infinite reaction network describing mass exchange between polymers. Serial transfer dynamics is typically used in molecular evolution experiments in the context of research on the origins of life. The present study is shedding a new light on the role played by serial transfer parameters in these experiments [1]. Time permitting we will also present another study of transient chemical reactors also motivated by research on the origins of life [2] [1] Reaction kinetics in open reactors and serial transfers between closed reactors A. Blokhuis, D. Lacoste, P. Gaspard, J. Chem. Phys. in press, https://arxiv.org/abs/1803.09548 [2] Selection dynamics in transient compartmentalization, A. Blokhuis, D. Lacoste, P. Nghe, L. Peliti, Phys. Rev. Lett. in press, https://arxiv.org/abs/1802.00208

In last two decades, several precise experimental tools have been developed to explore various thermodynamic properties of many modeled mesoscopic systems. In these modeled non-equilibrium systems, reaching the thermodynamic limit for work extraction and computations was possible only in arbitrary slow processes with carefully chosen reversible transformation protocols. Unlike modeled systems, common biological systems may not be able to reach ultimate thermodynamic limits because of additional constrains imposed by limited time, environmental noise, evolutionary development, access to resources, and many other metabolic processes. In this talk, I will present my work on measuring the thermodynamic efficiency of biological motor proteins. I use a nanopore-sequencing method to study a motor called PcrA helicase that unwinds a double-stranded DNA. This nanopore method captures a movement of one DNA strand through a nanopore as a helicase unwinds double-stranded DNA. I measure time that PcrA helicase needs to unwind different DNA sequences characterized by different binding energy and I further compare that with the actual energy spent in terms of number of ATP molecules consumed.

Under certain conditions, it takes a shorter time to cool a hot system than to cool the same system initiated at a lower temperature. This phenomenon — the “Mpemba effect” — was first observed in water and has recently been reported in other systems. Whereas several detail-dependent explanations were suggested for some of these observations, no common underlying mechanism is known. We present two widely applicable mechanism for similar effects, the Markovian Mpemba effect, derive the sufficient conditions for their appearance, and demonstrate them explicitly in the anti-ferromagnet Ising model. Interestingly, the Markovian Mpemba effect can be classified as ``weak'' or ``strong'' and as ``direct'' or ``inverse''. In the Ising model we show that the ``strong'' (direct and inverse) effect exists even in the thermodynamic limit.