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In nonequilibrium steady states of Markov jump processes, we derive exact Fluctuation-Response Relations (FRRs) that express the covariance between any pair of currents in terms of static responses in a notably simple form, thus generalizing the fluctuation-dissipation theorem far from equilibrium. We begin by considering perturbations in the symmetric part of the rates. We demonstrate that FRRs imply a hierarchy of thermodynamic bounds. These latter prove the recently conjectured Response Thermodynamic Uncertainty Relation (R-TUR), which bounds the ratio between any current's response and its variance by the entropy production rate (EPR). We furthermore strengthen this bound in two distinct ways, using partial EPR in one case and pseudo-EPR in the other. For perturbations in the antisymmetric part of the rates, we show that the ratio between any current's response and its variance is bounded by traffic, a metric representing the total number of transitions per unit time in the system. As an application, we use FRRs to explain the origin of positive correlations between currents in Coulomb-blockaded systems previously observed in experiments.

We investigate the multipartite mutual information between $N$ discrete-state stochastic units interacting in a networks that is invariant under unit permutations. We show that when the system relaxes to fixed point attractors, multipartite correlations in the stationary state either do not scale extensively with $N$, or the extensive scaling is not robust to small perturbations of the system parameters. In particular, robust extensive scaling cannot occur in thermodynamic equilibrium. In contrast, mutual information scales extensively when the system relaxes to time-dependent attractors (e.g., limit cycles), which can occur only far from equilibrium. This demonstrates the essential role of dissipation in the generation and maintenance of multipartite correlations. We illustrate our theory with the nonequilibrium Potts model., Comment: 7 pages, 2 figures

For overdamped Langevin systems subjected to weak thermal noise and nonconservative forces, we establish a connection between Freidlin-Wentzell large deviations theory and stochastic thermodynamics. First, we derive a series expansion of the quasipotential around the detailed-balance solution, i.e. the system's free energy, and identify the condition for the linear response regime to hold even far from equilibrium. Second, we prove that the escape rate from dissipative fixed points of the macroscopic dynamics is bounded by the entropy production of trajectories that relax into, and escape from the attractors. These results provide the foundation to study the nonequilibrium thermodynamics of dissipative metastable states.

We develop a framework describing the dynamics and thermodynamics of open non-ideal reaction-diffusion systems, which embodies Flory-Huggins theories of mixtures and chemical reaction network theories. Our theory elucidates the mechanisms underpinning the emergence of self-organized dissipative structures in these systems. It evaluates the dissipation needed to sustain and control them, discriminating the contributions from each reaction and diffusion process with spatial resolution. It also reveals the role of the reaction network in powering and shaping these structures. We identify particular classes of networks in which diffusion processes always equilibrate within the structures, while dissipation occurs solely due to chemical reactions. The spatial configurations resulting from these processes can be derived by minimizing a kinetic potential, contrasting with the minimization of the thermodynamic free energy in passive systems. This framework opens the way to investigating the energetic cost of phenomena such as liquid-liquid phase separation, coacervation, and the formation of biomolecular condensates.

There are conflicting reports in the literature regarding the finite-size scaling of the Liouvillian gap and dynamical fluctuations at discontinuous phase transitions, with various studies reporting either exponential or power-law behavior. We clarify this issue by employing large deviation theory. We distinguish two distinct classes of discontinuous phase transitions that have different dynamical properties. The first class is associated with phase coexistence, i.e., the presence of multiple stable attractors of the system dynamics (e.g., local minima of the free energy functional) in a finite phase diagram region around the phase transition point. In that case, one observes asymptotic exponential scaling related to stochastic switching between attractors (though the onset of exponential scaling may sometimes occur for very large system sizes). In the second class, there is no phase coexistence away from the phase transition point, while at the phase transition point itself there are infinitely many attractors. In that case, one observes power-law scaling related to the diffusive nature of the system relaxation to the stationary state., Comment: 20 pages, 20 figures. Accepted to Phys. Rev. E

The precision of currents in Markov networks is bounded by dissipation via the so-called thermodynamic uncertainty relation (TUR). In our work, we demonstrate a similar inequality that bounds the precision of the static current response to perturbations of kinetic barriers. Perturbations of such type, which affect only the system kinetics but not the thermodynamic forces, are highly important in biochemistry and nanoelectronics. We prove that our inequality cannot be derived from the standard TUR. Instead, it implies the standard TUR and provides an even tighter bound for dissipation. We also provide a procedure for obtaining the optimal response precision for a given model., Comment: 6 pages, 4 figures

We demonstrate that, for a chemical reaction network (CRN) engaged in energy transduction, its optimal operation from a thermodynamic efficiency standpoint is contingent upon its working conditions. Analogously to the bicycle gear system, CRNs have at their disposal several transducing mechanisms characterized by different yields. We highlight the critical role of the CRN's elementary flux modes in determining this "gearing" and their impact on maximizing energy transduction efficiency. Furthermore, we introduce an enzymatically regulated CRN, engineered to autonomously adjust its "gear", thereby optimizing its efficiency under different external conditions., Comment: 6 pages, 3 figures

We introduce a non-equilibrium version of the Caldeira-Leggett model in which a quantum particle is strongly coupled to a set of engineered reservoirs. The reservoirs are composed by collections of squeezed and displaced thermal modes, in contrast to the standard case in which the modes are assumed to be at equilibrium. The model proves to be very versatile. Strongly displaced/squeezed reservoirs can be used to generate an effective time dependence in the system Hamiltonian and can be identified as sources of pure work. In the case of squeezing, the time dependence is stochastic and breaks the fluctuation-dissipation relation, this can be reconciled with the second law of thermodynamics by correctly accounting for the energy used to generate the initial non-equilibrium conditions. To go beyond the average description and compute the full heat statistics, we treat squeezing and displacement as generalized Hamiltonians on a modified Keldysh contour. As an application of this technique, we show the quantum-classical correspondence between the heat statistics in the non-equilibrium Caldeira-Leggett model and the statistics of a classical Langevin particle under the action of squeezed and displaced colored noises. Finally, we discuss thermodynamic symmetries of the heat generating function, proving a fluctuation theorem for the energy balance and showing that the conservation of energy at the trajectory level emerges in the classical limit., Comment: 38 pages, 6 figures

Notable attention has been devoted to the problem of thermalization of observables in isolated quantum setups by individual eigenstates. Here, we approach this issue from an open quantum system perspective, by considering isolated setups which consists of a small system coupled to a macroscopic bath. We argue that in such a case, even in fully integrable models, the system observables exhibit thermalization when the system-bath setup is in a typical eigenstate of its Hamiltonian (which is called weak eigenstate thermalization). This occurs unless thermalization is suppressed by localization due to strong coupling. We illustrate our claim for a single fermionic level coupled to a noninteracting fermionic bath. We further show that upon quenching the system Hamiltonian, the system occupancy typically relaxes to the thermal value corresponding to the new Hamiltonian. Finally, we demonstrate that system thermalization also arises for a system coupled to a bath initialized in a typical eigenstate of its Hamiltonian. Our findings suggest that chaos and nonintegrability are not the sole drivers of thermalization and complementary approaches are needed to offer a more comprehensive understanding of how statistical mechanics emerges., Comment: 15 pages, 12 figures

We explore the critical properties of the recently discovered finite-time dynamical phase transition in the non-equilibrium relaxation of Ising magnets. The transition is characterized by a sudden switch in the relaxation dynamics and it occurs at a sharp critical time. While previous works have focused either on mean-field interactions or on investigating the properties of the critical time, we analyze the critical fluctuations at the phase transition in the nearest-neighbor Ising model on a square lattice using Monte Carlo simulations. By means of a finite-size scaling analysis, we extract the critical exponents for the transition. In two spatial dimensions, the exponents are consistent with those of the two-dimensional Ising universality class., Comment: 11 pages, 7 figures

We consider Markov jump processes on a graph described by a rate matrix that depends on various control parameters. We derive explicit expressions for the static responses of edge currents and steady-state probabilities. We show that they are constrained by the graph topology (i.e. the incidence matrix) by deriving response relations (i.e. linear constraints linking the different responses) and topology-dependent bounds. For unicyclic networks, all scaled current responses are between zero and one and must sum to one. Applying these results to stochastic thermodynamics, we derive explicit expressions for the static response of fundamental currents (which carry the full dissipation) to fundamental thermodynamic forces (which drive the system away from equilibrium)., Comment: Accepted to Physical Review Letters

We derive a systematic approach to the thermodynamics of quantum systems based on the underlying symmetry groups. We show that the entropy of a system can be described in terms of group-theoretical quantities that are largely independent of the details of its density matrix. We apply our technique to generic $N$ identical interacting $d$-level quantum systems. Using permutation invariance, we find that, for large $N$, entropy displays a universal large deviation behavior with a rate function $s(\boldsymbol{x})$ that is completely independent of the microscopic details of the model, but depends only on the size of the irreducible representations of the permutation group $\text{S}_N$. In turn, the partition function is shown to satisfy a large deviation principle with a free energy $f(\boldsymbol{x})=e(\boldsymbol{x})-\beta^{-1}s(\boldsymbol{x})$, where $e(\boldsymbol{x})$ is a rate function that only depends on the ground state energy of particular subspaces determined by group representation theory. We apply our theory to the transverse-field Curie-Weiss model, a minimal model of phase transition exhibiting an interplay of thermal and quantum fluctuations., Comment: 10 pages, 2 figures

We prove a linear stability-dissipation relation (SDR) for $q$-state Potts models driven far from equilibrium by a nonconservative force. At a critical coupling strength, these models exhibit a synchronisation transition from a decoherent into a synchronised state. In the vicinity of this transition, the SDR connects the entropy production rate per oscillator to the phase-space contraction rate, a measure of stability, in a simple way. For large but finite systems, the SDR implies a minimum-dissipation principle for driven Potts models as the dynamics selects stable non-equilibrium states with least dissipation. This principle holds arbitrarily far from equilibrium, for any stochastic dynamics, and for all $q$., Comment: 6 pages, 4 figures, 3 supplemental videos

We study driven $q$-state Potts models with thermodynamically consistent dynamics and global coupling. For a wide range of parameters, these models exhibit a dynamical phase transition from decoherent oscillations into a synchronised phase. Starting from a general microscopic dynamics for individual oscillators, we derive the normal form of the high-dimensional Hopf-Bifurcation that underlies the phase transition. The normal-form equations are exact in the thermodynamic limit and close to the bifurcation. Making use of the symmetry of the model, we solve these equations analytically and thus uncover the intricate stable synchronisation patterns of driven Potts models, characterised by a rich phase diagram. Making use of thermodynamic consistency, we show that synchronisation reduces dissipation in such a way that the most stable synchronised states dissipate the least entropy. Close to the phase transition, our findings condense into a linear dissipation-stability relation that connects entropy production with phase-space contraction, a stability measure. At finite system size, our findings suggest a minimum-dissipation principle for driven Potts models that holds arbitrarily far from equilibrium., Comment: 23 pages, 9 Figures

Lecture notes after the doctoral school (Post)Modern Thermodynamics held at the University of Luxembourg, December 2022, 5-7, covering and advancing continuous-time Markov chains, network theory, stochastic thermodynamics, large deviations, deterministic and stochastic chemical reaction networks, metastability, martingales, quantum thermodynamics, and foundational issues., Comment: Submission to SciPost

The thermodynamic and dynamical conditions necessary to observe indefinite growth in homogeneous open chemical reaction networks (CRNs) satisfying mass action kinetics were presented in Srinivas et al. (2023): Unimolecular CRNs can only accumulate equilibrium concentrations of species while multimolecular CRNs are needed to produce indefinite growth with nonequilibrium concentrations. Within multimolecular CRNs, pseudo-unimolecular CRNs produce nonequilibrium concentrations with zero efficiencies. Nonequilibrium growth with finite efficiencies requires dynamically nonlinear CRNs. In this paper, we provide a detailed analysis supporting these results. Mathematical proofs are provided for growth in unimolecular and pseudo-unimolecular CRNs. For multimolecular CRNs, four models displaying very distinctive topological properties are extensively studied, both numerically and partly analytically.

We identify the thermodynamic conditions necessary to observe indefinite growth in homogeneous open chemical reaction networks (CRNs) satisfying mass action kinetics. We also characterize the thermodynamic efficiency of growth by considering the fraction of the chemical work supplied from the surroundings that is converted into CRN free energy. We find that indefinite growth cannot arise in CRNs chemostatted by fixing the concentration of some species at constant values, or in continuous-flow stirred tank reactors. Indefinite growth requires a constant net influx from the surroundings of at least one species. In this case, unimolecular CRNs always generate equilibrium linear growth, i.e., a continuous linear accumulation of species with equilibrium concentrations and efficiency one. Multimolecular CRNs are necessary to generate nonequilibrium growth, i.e., the continuous accumulation of species with nonequilibrium concentrations. Pseudo-unimolecular CRNs - a subclass of multimolecular CRNs - always generate asymptotic linear growth with zero efficiency. Our findings demonstrate the importance of the CRN topology and the chemostatting procedure in determining the dynamics and thermodynamics of growth.

Based on exact integration of the Schr\"odinger equation, we numerically study microscopic contributions to the entropy production for the single electron transistor, a paradigmatic model describing a single Fermi level tunnel coupled to two baths of free fermions. To this end, we decompose the entropy production into a sum of information theoretic terms and study them across all relevant time scales, including the nonequilibrium steady state regime and the final stage of global thermalization. We find that the entropy production is dominated for most times by microscopic deviations from thermality in the baths and the correlation between (but not inside) the baths. Despite these microscopic deviations from thermality, the temperatures and chemical potentials of the baths thermalize as expected, even though our model is integrable. Importantly, this observation is confirmed for both initially mixed and pure states. We further observe that the bath-bath correlations are quite insensitive to the system-bath coupling strength contrary to intuition. Finally, the system-bath correlation, small in an absolute sense, dominates in a relative sense and displays pure quantum correlations for all studied parameter regimes., Comment: 12 pages, 9 figures

Clocks are inherently out-of-equilibrium because, due to friction, they constantly consume free energy to keep track of time. The Thermodynamic Uncertainty Relation (TUR) quantifies the trade-off between the precision of any time-antisymmetric observable and entropy production. In the context of clocks, the TUR implies that a minimum entropy production is needed in order to achieve a certain level of precision in timekeeping. But the TUR has only been proven for overdamped systems. Recently, a toy model of a classical underdamped pendulum clock was proposed that violated this relation (Phys. Rev. Lett. 128, 130606), thus demonstrating that the TUR does not hold for underdamped dynamics. We propose an electronic implementation of such a clock, using a resistor-inductor-capacitor (RLC) circuit and a biased CMOS inverter (NOT gate), which can work at different scales. We find that in the nanoscopic single-electron regime of the circuit, we essentially recover the toy model violating the TUR bound. However, in different macroscopic regimes of the circuit, we show that the TUR bound is restored and analyze the thermodynamic efficiency of timekeeping., Comment: 20 pages, 10 figures

Generalizing response theory of open systems far from equilibrium is a central quest of nonequilibrium statistical physics. Using stochastic thermodynamics, we develop an algebraic method to study the response of nonequilibrium steady state to arbitrary perturbations. This allows us to derive explicit expressions for the response of edge currents as well as traffic to perturbations in kinetic barriers and driving forces. We also show that these responses satisfy very simple bounds. For the response to energy perturbations, we straightforwardly recover results obtained using nontrivial graph-theoretical methods.

We study an autonomous model of a Maxwell demon that works by rectifying thermal fluctuations of chemical reactions. It constitutes the chemical analog of a recently studied electronic demon. We characterize its scaling behavior in the macroscopic limit, its performances, and the impact of potential internal delays. We obtain analytical expressions for all quantities of interest, namely, the generated reverse chemical current, the output power, the transduction efficiency, and the correlations between the numbers of molecules. Due to a bound on the nonequilibrium response of its chemical reaction network, we find that, contrary to the electronic case, there is no way for the Maxwell demon to generate a finite output in the macroscopic limit. Finally, we analyze the information thermodynamics of the Maxwell demon from a bipartite perspective. In the limit of a fast demon, the information flow is obtained, its pattern in the state space is discussed, and the behavior of the partial efficiencies related to the measurement and the feedback processes is examined., Comment: 16 pages, 3 figures

Starting at the mesoscopic level with a general formulation of stochastic thermodynamics in terms of Markov jump processes, we identify the scaling conditions that ensure the emergence of a (typically nonlinear) deterministic dynamics and an extensive thermodynamics at the macroscopic level. We then use large deviations theory to build a macroscopic fluctuation theory around this deterministic behavior, which we show preserves the fluctuation theorem. For many systems (e.g. chemical reaction networks, electronic circuits, Potts models), this theory does not coincide with Langevin-equation approaches (obtained by adding Gaussian white noise to the deterministic dynamics) which, if used, are thermodynamically inconsistent. Einstein-Onsager theory of Gaussian fluctuations and irreversible thermodynamics are recovered at equilibrium and close to it, respectively. Far from equilibirum, the free energy is replaced by the dynamically generated quasi-potential (or self-information) which is a Lyapunov function for the macroscopic dynamics. Remarkably, thermodynamics connects the dissipation along deterministic and escape trajectories to the Freidlin-Wentzell quasi-potential, thus constraining the transition rates between attractors induced by rare fluctuations. A coherent perspective on minimum and maximum entropy production principles is also provided. For systems that admit a continuous-space limit, we derive a nonequilibrium fluctuating field theory with its associated thermodynamics. Finally, we coarse grain the macroscopic stochastic dynamics into a Markov jump process describing transitions among deterministic attractors and formulate the stochastic thermodynamics emerging from it., Comment: Applications added

We investigate the behavior of entanglement between a single fermionic level and a fermionic bath in three distinct thermodynamic regimes. First, in thermal equilibrium, we analyze the dependence of entanglement on the considered statistical ensemble: for the grand canonical state, it is generated only for a sufficiently strong system-bath coupling, whereas it is present for arbitrarily weak couplings for the canonical state with a fixed particle number. The threshold coupling strength, at which entanglement appears, is shown to strongly depend on the bath bandwidth. Second, we consider the relaxation to equilibrium. In this case a transient entanglement in a certain time interval can be observed even in the weak-coupling regime, when the reduced dynamics and thermodynamics of the system can be well described by an effectively classical and Markovian master equation for the state populations. At strong coupling strengths, entanglement is preserved for long times and converges to its equilibrium value. Finally, in voltage-driven junctions, a steady-state entanglement is generated for arbitrarily weak system-bath couplings at a certain threshold voltage. It is enhanced in the strong-coupling regime, and it is reduced by either the particle-hole or the tunnel coupling asymmetry., Comment: 26 pages, 29 figures. It includes content from arXiv:2306.08626

We investigate the dynamics of entanglement between the system and the environment during thermalization of a noninteracting fermionic impurity coupled to a fermionic thermal bath. We show that transient entanglement can be observed even in the weak coupling regime, when the reduced dynamics and thermodynamics of the system can be well described by an effectively classical and Markovian master equation for the state populations. This entanglement vanishes for long times, but is preserved over timescales comparable to the relaxation time. Its magnitude depends only weakly on the system-environment coupling but instead strongly on the purity of the initial state of the system. We relate the presence of such transient entanglement to the unitary character of the system-bath dynamics underlying the reduced Markovian description., Comment: The content of the paper has been integrated into arXiv:2306.09680

We show that macroscopic irreversible thermodynamics for viscous fluids can be derived from exact information-theoretic thermodynamic identities valid at the microscale. Entropy production, in particular, is a measure of the loss of many-particle correlations in the same way in which it measures the loss of system-reservoirs correlations in stochastic thermodynamics (ST). More specifically, we first show that boundary conditions at the macroscopic level define a natural decomposition of the entropy production rate (EPR) in terms of thermodynamic forces multiplying their conjugate currents, as well as a change in suitable nonequilibrium potential that acts as a Lyapunov function in the absence of forces. Moving to the microscale, we identify the exact identities at the origin of these dissipative contributions for isolated Hamiltonian systems. We then show that the molecular chaos hypothesis, which gives rise to the Boltzmann equation at the mesoscale, leads to a positive rate of loss of many-particle correlations, which we identify with the Boltzmann EPR. By generalizing the Boltzmann equation to account for boundaries with nonuniform temperature and nonzero velocity, and resorting to the Chapman-Enskog expansion, we recover the macroscopic theory we started from. Finally, using a linearized Boltzmann equation we derive ST for dilute particles in a weakly out-of-equilibrium fluid and its corresponding macroscopic thermodynamics. Our work unambiguously demonstrates the information-theoretical origin of thermodynamic notions of entropy and dissipation in macroscale irreversible thermodynamics., Comment: 36 pages, 1 figure

We develop a general classification of the nature of the instabilities yielding spatial organization in open nonideal reaction-diffusion systems, based on linear stability analysis. This encompasses dynamics where chemical species diffuse, interact with each other, and undergo chemical reactions driven out of equilibrium by external chemostats. We find analytically that these instabilities can be of two types: instabilities caused by intermolecular energetic interactions (E type), and instabilities caused by multimolecular out-of-equilibrium chemical reactions (R type). Furthermore, we identify a class of chemical reaction networks, containing unimolecular networks but also extending beyond them, that can only undergo E-type instabilities. We illustrate our analytical findings with numerical simulations on two reaction-diffusion models, each displaying one of the two types of instability and generating stable patterns.

The work fluctuation theorem (FT) is a symmetry connecting the moment generating functions (MGFs) of the work extracted in a given process and in its time-reversed counterpart. We show that, equivalently, the FT for work in isolated quantum systems can be expressed as an invariance property of a modified Keldysh contour. Modified contours can be used as starting points of perturbative and path integral approaches to quantum thermodynamics, as recently pointed out in the literature. After reviewing the derivation of the contour-based perturbation theory, we use the symmetry of the modified contour to show that the theory satisfies the FT at every order. Furthermore, we extend textbook diagrammatic techniques to the computation of work MGFs, showing that the contributions of the different Feynman diagrams can be added to obtain a general expression of the work statistics in terms of a sum of independent rescaled Poisson processes. In this context, the FT takes the form of a detailed balance condition linking every Feynman diagram with its time-reversed variant. In the second part, we study path integral approaches to the calculation of the MGF, and discuss how the arbitrariness in the choice of the contour impacts the final form of the path integral action. In particular, we show how using a symmetrized contour makes it possible to easily generalize the Keldysh rotation in the context of work statistics, a procedure paving the way to a semiclassical expansion of the work MGF. Furthermore, we use our results to discuss a generalization of the detailed balance conditions at the level of the quantum trajectories., Comment: 45 pages, 6 figures. New version after the first round of review; minor corrections have been made, some new references have been added to the bibliography

We study a model of synthetic molecular motor - a [3]-catenane consisting of two small macrocycles mechanically interlocked with a bigger one - subjected to a time-dependent driving using stochastic thermodynamics. The model presents nontrivial features due to the two interacting small macrocycles, but is simple enough to be treated analytically in limiting regimes. Among the results obtained, we find a mapping into an equivalent [2]-catenane that reveals the implications of the no-pumping theorem stating that to generate net motion of the small macrocycles, both energies and barriers need to change. In the adiabatic limit (slow driving), we fully characterize the motor's dynamics and show that the net motion of the small macrocycles is expressed as a surface integral in parameter space which corrects previous erroneous results. We also analyze the performance of the motor subjected to a step-wise driving protocols in absence and in presence of an applied load. Optimization strategies for generating large currents and maximizing free-energy transduction are proposed. This simple model provides interesting clues into the working principles of non-autonomous molecular motors and their optimization., Comment: 14 pages, 5 figures

As previously demonstrated, the entropy production -- a key quantity characterizing the irreversibility of thermodynamic processes -- is related to generation of correlations between degrees of freedom of the system and its thermal environment. This raises the question of whether such correlations are of a classical or quantum nature, namely, whether they are accessible through local measurements on the correlated degrees of freedom. We address this problem by considering fermionic and bosonic Gaussian systems. We show that for fermions the entropy production is mostly quantum due to the parity superselection rule which restricts the set of physically allowed measurements to projections on the Fock states, thus significantly limiting the amount of classically accessible correlations. In contrast, in bosonic systems a much larger amount of correlations can be accessed through Gaussian measurements. Specifically, while the quantum contribution may be important at low temperatures, in the high temperature limit the entropy production corresponds to purely classical position-momentum correlations. Our results demonstrate an important difference between fermionic and bosonic systems regarding the existence of a quantum-to-classical transition in the microscopic formulation of the entropy production. They also show that entropy production can be mainly caused by quantum correlations even in the weak coupling limit, which admits a description in terms of classical rate equations for state populations, as well as in the low particle density limit, where the transport properties of both bosons and fermions converge to those of classical particles., Comment: 23 pages, 17 figures

Living organisms continuously harness energy to perform complex functions for their adaptation and survival while part of that energy is dissipated in the form of heat or chemical waste. Determining the energetic cost and the efficiency of specific cellular processes remains a largely open problem. Here, we analyze the efficiency of mitochondrial adenosine triphosphate (ATP) production through the tricarboxylic acid (TCA) cycle and oxidative phosphorylation that generates most of the cellular chemical energy in eukaryotes. The regulation of this pathway by calcium signaling represents a well-characterized example of a regulatory cross-talk that can affect the energetic output of a metabolic pathway, but its concrete energetic impact remains elusive. On the one hand, calcium enhances ATP production by activating key enzymes of the TCA cycle, but on the other hand calcium homeostasis depends on ATP availability. To evaluate how calcium signaling impacts the efficiency of mitochondrial metabolism, we propose a detailed kinetic model describing the calcium-mitochondria cross-talk and we analyze it using a nonequilibrium thermodynamic approach: after identifying the effective reactions driving mitochondrial metabolism out of equilibrium, we quantify the thermodynamic efficiency of the metabolic machinery for different physiological conditions. We find that calcium oscillations increase the efficiency with a maximum close to substrate-limited conditions, suggesting a compensatory effect of calcium signaling on the energetics of mitochondrial metabolism.

Stochastic chemical processes are described by the chemical master equation satisfying the law of mass-action. We first ask whether the dual master equation, which has the same steady state as the chemical master equation, but with inverted reaction currents, satisfies the law of mass-action, namely, still describes a chemical process. We prove that the answer depends on the topological property of the underlying chemical reaction network known as deficiency. The answer is yes only for deficiency-zero networks. It is no for all other networks, implying that their steady-state currents cannot be inverted by controlling the kinetic constants of the reactions. Hence, the network deficiency imposes a form of non-invertibility to the chemical dynamics. We then ask whether catalytic chemical networks are deficiency-zero. We prove that the answer is no when they are driven out of equilibrium due to the exchange of some species with the environment.

We show that the energy statistics resulting from a two-point measurement of an isolated quantum system subject to a time-dependent driving protocol can be probed by subjecting the same system to a collision with a suitably prepared incoming particle. This means that the particle acts both as an external drive and as an energy measurement device for the quantum system and that energy fluctuations can be defined within a fully autonomous setting., Comment: 6 Pages, 1 figures. Final version published in Physical Review Research

We introduce a wide class of quantum maps that arise in collisional reservoirs and are able to thermalize a system if they operate in conjunction with an additional dephasing mechanism. These maps describe the effect of collisions and induce transitions between populations that obey detailed balance, but also create coherences that prevent the system from thermalizing. We combine these maps with a unitary evolution acting during random Poissonian times between collisions and causing dephasing. We find that, at a low collision rate, the nontrivial combination of these two effects causes thermalization in the system. This scenario is suitable for modeling collisional reservoirs at equilibrium. We justify this claim by identifying the conditions for such maps to arise within a scattering theory approach and provide a thorough characterization of the resulting thermalization process., Comment: 5 pages, 3 figures

The entropy production of an open system coupled to a reservoir initialized in a canonical state can be expressed as a sum of two microscopic information-theoretic contributions: the system-bath mutual information and the relative entropy measuring the displacement of the environment from equilibrium. We investigate whether this result can be generalized to situations where the reservoir is initialized in a microcanonical or in a certain pure state (e.g., an eigenstate of a nonintegrable system), such that the reduced dynamics and thermodynamics of the system are the same as for the thermal bath. We show that while in such a case the entropy production can still be expressed as a sum of the mutual information between the system and the bath and a properly redefined displacement term, the relative weight of those contributions depends on the initial state of the reservoir. In other words, different statistical ensembles for the environment predicting the same reduced dynamics for the system give rise to the same total entropy production but to different information-theoretic contributions to the entropy production., Comment: 6 pages, 3 figures, with Supplemental Material

There is ongoing controversy about whether a coherent superposition of the occupied states of two fermionic modes should be regarded entangled or not, that is, whether its intrinsic quantum correlations are operationally accessible and useful as a resource. This has been questioned on the basis that such an entanglement cannot be accessed by local operations on individual modes due to the parity superselection rule which constrains the set of physical observables. In other words, one cannot observe violations of Bell's inequality. Here we show, however, that entanglement of a two-mode fermionic state can be used as a genuine quantum resource in open-system thermodynamic processes, enabling one to perform tasks forbidden for separable states. We thus demonstrate that quantum thermodynamics can shed light on the nature of fermionic entanglement and the operational meaning of the different notions used to define it., Comment: 6 pages, 2 figures

A CMOS-based implementation of an autonomous Maxwell's demon was recently proposed (Phys. Rev. Lett. 129, 120602) to demonstrate that a Maxwell demon can still work at macroscopic scales, provided that its power supply is scaled appropriately. Here, we first provide a full analytical characterization of the non-autonomous version of that model. We then study system-demon information flows within generic autonomous bipartite setups displaying a macroscopic limit. By doing so, we can study the thermodynamic efficiency of both the measurement and the feedback process performed by the demon. We find that the information flow is an intensive quantity and that, as a consequence, any Maxwell's demon is bound to stop working above a finite scale if all parameters but the scale are fixed. However, this can be prevented by appropriately scaling the thermodynamic forces. These general results are applied to the autonomous CMOS-based demon., Comment: minor corrections. arXiv admin note: text overlap with arXiv:2204.09466

We lay the foundation of a circuit theory for chemical reaction networks. Chemical reactions are grouped into chemical modules solely characterized by their current-concentration characteristic, as electrical devices by their current-voltage (I-V) curve in electronic circuit theory. This, combined with the chemical analog of Kirchhoff's current and voltage laws, provides a powerful tool to predict reaction currents and dissipation across complex chemical networks. The theory can serve to build accurate reduced models of complex networks as well as to design networks performing desired tasks.

Starting from a microscopic system-baths description, we derive the general conditions for a time-local quantum master equation (QME) to satisfy the first and second law of thermodynamics at the fluctuating level. Using counting statistics, we show that the fluctuating second law can be rephrased as a Generalized Quantum Detailed Balance condition (GQDB), i.e., a symmetry of the time-local generators which ensures the validity of the fluctuation theorem. When requiring in addition a strict system-bath energy conservation, the GQDB reduces to the usual notion of detailed balance which ensures QMEs with Gibbsian steady states. However, if energy conservation is only required on average, QMEs with non Gibbsian steady states can still maintain a certain level of thermodynamic consistency. Applying our theory to commonly used QMEs, we show that the Redfield equation breaks the GQDB, and that some recently derived approximation schemes based on the Redfield equation (which hold beyond the secular approximation and allow to derive a QME of Lindblad form) satisfy the GQDB and the average first law. We find that performing the secular approximation is the only way to ensure the first and second law at the fluctuating level.

We study the thermodynamics of open systems weakly driven out-of-equilibrium by nonconservative and time-dependent forces using the linear regime of stochastic thermodynamics. We make use of conservation laws to identify the potential and nonconservative components of the forces. This allows us to formulate a unified near-equilibrium thermodynamics. For nonequilibrium steady states, we obtain an Onsager theory ensuring nonsingular response matrices that is consistent with phenomenological linear irreversible thermodynamics. For time-dependent driving protocols that do not produce nonconservative forces, we identify the equilibrium ensemble from which Green-Kubo relations are recovered. For arbitrary periodic drivings, the averaged entropy production (EP) is expressed as an independent sum over each driving frequency of non-negative contributions. These contributions are bilinear in the nonconservative and conservative forces and involve a novel generalized Onsager matrix that is symmetric. In the most general case of arbitrary time-dependent drivings, we advance a novel decomposition of the EP rate into two non-negative contributions - one solely due to nonconservative forces and the other solely due to deviation from the instantaneous steady-state - directly implying a minimum entropy production principle close to equilibrium. This setting reveals the geometric structure of near-equilibrium thermodynamics and generalizes previous approaches to cases with nonconservative forces., Comment: 25 pages, 5 figures

The latest generation of transistors are nanoscale devices whose performance and reliability are limited by thermal noise in low-power applications. Therefore developing efficient methods to compute the voltage and current fluctuations in such non-linear electronic circuits is essential. Traditional approaches commonly rely on adding Gaussian white noise to the macroscopic dynamical circuit laws, but do not capture rare fluctuations and lead to thermodynamic inconsistencies. A correct and thermodynamically consistent approach can be achieved by describing single-electron transfers as Poisson jump processes accounting for charging effects. But such descriptions can be computationally demanding. To address this issue, we consider the macroscopic limit which corresponds to scaling up the physical dimensions of the transistor and resulting in an increase of the number of electrons on the conductors. In this limit, the thermal fluctuations satisfy a Large Deviations Principle which we show is also remarkably precise in settings involving only a few tens of electrons, by comparing our results with Gillespie simulations and spectral methods. Traditional approaches are recovered by resorting to an ad hoc diffusive approximation introducing inconsistencies. To illustrate these findings, we consider a low-power CMOS inverter, or NOT gate, which is a basic primitive in electronic design. Voltage (resp. current) fluctuations are obtained analytically (semi-analytically) and reveal interesting features.

We study the time evolution of thermodynamic observables that characterise the dissipative nature of thermal relaxation after an instantaneous temperature quench. Combining tools from stochastic thermodynamics and large-deviation theory, we develop a powerful theory for computing the large-deviation statistics of such observables. Our method naturally leads to a description in terms of a dynamical Landau theory, a versatile tool for the analysis of finite-time dynamical phase transitions. The topology of the associated Landau potential allows for an unambiguous identification of the dynamical order parameter and of the phase diagram. As an immediate application of our method, we show that the probability distribution of the heat exchanged between a mean-field spin model and the environment exhibits a singular point, a kink, caused by a finite-time dynamical phase transition. Using our Landau theory, we conduct a detailed study of the phase transition. Although the manifestation of the new transition is similar to that of a previously found finite-time transition in the magnetisation, the properties and the dynamical origins of the two turn out to be very different., Comment: 30 pages, 9 figures

It is commonly accepted that exoplanets with orbital periods shorter than 1 day, also known as ultra-short period (USP) planets, formed further out within their natal protoplanetary disk, before migrating to their current-day orbits via dynamical interactions. One of the most accepted theories suggests a violent scenario involving high-eccentricity migration followed by tidal circularization. Here, we present the discovery of a four planet system orbiting the bright (V=10.5) K6 dwarf star TOI-500. The innermost planet is a transiting, Earth-sized USP planet with an orbital period of $\sim$ 13 hours, a mass of 1.42 $\pm$ 0.18 M$_{\oplus}$, a radius of $1.166^{0.061}_{-0.058}$ R$_{\oplus}$, and a mean density of 4.89$^{+1.03}_{-0.88}$ gcm$^{-3}$. Via Doppler spectroscopy, we discovered that the system hosts three outer planets on nearly circular orbits with periods of 6.6, 26.2, and 61.3d and minimum masses of 5.03 $\pm$ 0.41 M$_{\oplus}$, 33.12 $\pm$ 0.88 M$_{\oplus}$ and 15.05$^{+1.12}_{-1.11}$ M$_{\oplus}$, respectively. The presence of both a USP planet and a low-mass object on a 6.6-day orbit indicates that the architecture of this system can be explained via a scenario in which the planets started on low-eccentricity orbits, then moved inwards through a quasi-static secular migration. Our numerical simulations show that this migration channel can bring TOI-500 b to its current location in 2 Gyrs, starting from an initial orbit of 0.02au. TOI-500 is the first four planet system known to host a USP Earth analog whose current architecture can be explained via a non-violent migration scenario., Comment: Published on Nature Astronomy (April 28th, 2022)

Maxwell's demons work by rectifying thermal fluctuations. They are not expected to function at macroscopic scales where fluctuations become negligible and dynamics become deterministic. We propose an electronic implementation of an autonomous Maxwell's demon that indeed stops working in the regular macroscopic limit as the dynamics becomes deterministic. However, we find that if the power supplied to the demon is scaled up appropriately, the deterministic limit is avoided and the demon continues to work. The price to pay is a decreasing thermodynamic efficiency. Our work suggests that novel strategies may be found in nonequilibrium settings to bring to the macroscale non-trivial effects so far only observed at microscopic scales.

Information thermodynamics relates the rate of change of mutual information between two interacting subsystems to their thermodynamics when the joined system is described by a bipartite stochastic dynamics satisfying local detailed balance. Here, we expand the scope of information thermodynamics to deterministic bipartite chemical reaction networks, namely, composed of two coupled subnetworks sharing species, but not reactions. We do so by introducing a meaningful notion of mutual information between different molecular features, that we express in terms of deterministic concentrations. This allows us to formulate separate second laws for each subnetwork, which account for their energy and information exchanges, in complete analogy with stochastic systems. We then use our framework to investigate the working mechanisms of a model of chemically-driven self-assembly and an experimental light-driven bimolecular motor. We show that both systems are constituted by two coupled subnetworks of chemical reactions. One subnetwork is maintained out of equilibrium by external reservoirs (chemostats or light sources) and powers the other via energy and information flows. In doing so, we clarify that the information flow is precisely the thermodynamic counterpart of an information ratchet mechanism only when no energy flow is involved., Comment: 18 pages, 3 figures

We report the discovery of two transiting planets around the bright ($V=9.9$ mag) main sequence F7 star TOI-1670 by the Transiting Exoplanet Survey Satellite. TOI-1670 b is a sub-Neptune ($R_\mathrm{b} = 2.06_{-0.15}^{+0.19}$ $R_\oplus$) on a 10.9-day orbit and TOI-1670 c is a warm Jupiter ($R_\mathrm{c} = 0.987_{-0.025}^{+0.025}$ $R_\mathrm{Jup}$) on a 40.7-day orbit. Using radial velocity observations gathered with the Tull coud\'e Spectrograph on the Harlan J. Smith telescope and HARPS-N on the Telescopio Nazionale Galileo, we find a planet mass of $M_\mathrm{c} = 0.63_{-0.08}^{+0.09}$ $M_\mathrm{Jup}$ for the outer warm Jupiter, implying a mean density of $\rho_c = 0.81_{-0.11}^{+0.13}$ g cm$^{-3}$. The inner sub-Neptune is undetected in our radial velocity data ($M_\mathrm{b} < 0.13$ $M_\mathrm{Jup}$ at the 99% confidence level). Multi-planet systems like TOI-1670 hosting an outer warm Jupiter on a nearly circular orbit ($e_\mathrm{c} = 0.09_{-0.04}^{+0.05}$) and one or more inner coplanar planets are more consistent with "gentle" formation mechanisms such as disk migration or $in$ $situ$ formation rather than high-eccentricity migration. Of the 11 known systems with a warm Jupiter and a smaller inner companion, 8 (73%) are near a low-order mean-motion resonance, which can be a signature of migration. TOI-1670 joins two other systems (27% of this subsample) with period commensurabilities greater than 3, a common feature of $in$ $situ$ formation or halted inward migration. TOI-1670 and the handful of similar systems support a diversity of formation pathways for warm Jupiters., Comment: 23 pages, 9 figures, accepted for publication in AJ

Pi Men hosts a transiting planet detected by the TESS space mission and an outer planet in a 5.7-yr orbit discovered by RV surveys. We studied this system using new radial velocity (RV) measurements taken with the HARPS spectrograph on ESO's 3.6-m telescope as well as archival data. We constrain the stellar RV semi-amplitude due to the transiting planet, Pi Men c, as K_c = 1.21 +/- 0.12 m/s resulting in a planet mass of M_c = 3.63 +/- 0.38 M_Earth. A planet radius of R_c= 2.145 +/- 0.015 R_Earth yields a bulk density of rho = 2.03 +/- 0.22 g/cm^{-3}. The precisely determined density of this planet and the brightness of the host star make Pi Men c an excellent laboratory for internal structure and atmospheric characterization studies. Our HARPS RV measurements also reveal compelling evidence for a third body, PI Men d, with a minimum mass M sin i = 13.38 +/- 1.35 M_Earth orbiting with a period of P_d = 125 d on an eccentric orbit (e = 0.22). A simple dynamical analysis indicates that the orbit of Pi Men d is stable on timescales of at least 20 Myrs. Given the mutual inclination between the outer gaseous giant and the inner rocky planet and the presence of a third body at 125 d, Pi Men is an important planetary system for dynamical and formation studies., Comment: Accepted for publication in the Astronomical Journal. 40 pages, 16 figures

We provide a rigorous definition of free-energy transduction and its efficiency in arbitrary -- linear or nonlinear -- open chemical reaction networks (CRNs) operating at steady state. Our method is based on the knowledge of the stoichiometric matrix and of the chemostatted species (i.e. the species maintained at constant concentration by the environment) to identify the fundamental currents and forces contributing to the entropy production. Transduction occurs when the current of a stoichiometrically balanced process is driven against its spontaneous direction (set by its force) thanks to other processes flowing along their spontaneous direction. In these regimes, open CRNs operate as thermodynamic machines. After exemplifying these general ideas using toy models, we analyze central energy metabolism. We relate the fundamental currents to metabolic pathways and discuss the efficiency with which they are able to transduce free energy., Comment: 17 pages, 17 figues, (v2: IV.A.3 & IV.C modified, VI expanded)