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Collective Power: Minimal Model for Thermodynamics of Nonequilibrium Phase Transitions Herpich, Tim ; ; Esposito, Massimiliano in Physical Review. X (2018), 8(3), 031056 We propose a thermodynamically consistent minimal model to study synchronization which is made of driven and interacting three-state units. This system exhibits at the mean-field level two bifurcations ... [more ▼] We propose a thermodynamically consistent minimal model to study synchronization which is made of driven and interacting three-state units. This system exhibits at the mean-field level two bifurcations separating three dynamical phases: a single stable fixed point, a stable limit cycle indicative of synchronization, and multiple stable fixed points. These complex emergent dynamical behaviors are understood at the level of the underlying linear Markovian dynamics in terms of metastability, i.e. the appearance of gaps in the upper real part of the spectrum of the Markov generator. Stochastic thermodynamics is used to study the dissipated work across dynamical phases as well as across scales. This dissipated work is found to be reduced by the attractive interactions between the units and to nontrivially depend on the system size. When operating as a work-to- work converter, we find that the maximum power output is achieved far-from-equilibrium in the synchronization regime and that the efficiency at maximum power is surprisingly close to the linear regime prediction. Our work shows the way towards building a thermodynamics of nonequilibrium phase transitions in conjunction to bifurcation theory. [less ▲] Detailed reference viewed: 120 (17 UL)Information Thermodynamics of Turing Patterns Falasco, Gianmaria ; Rao, Riccardo ; Esposito, Massimiliano in Physical Review Letters (2018) e set up a rigorous thermodynamic description of reaction-diffusion systems driven out of equilibrium by time-dependent space-distributed chemostats. Building on the assumption of local equilibrium ... [more ▼] e set up a rigorous thermodynamic description of reaction-diffusion systems driven out of equilibrium by time-dependent space-distributed chemostats. Building on the assumption of local equilibrium, nonequilibrium thermodynamic potentials are constructed exploiting the symmetries of the chemical network topology. It is shown that the canonical (resp. semigrand canonical) nonequilibrium free energy works as a Lyapunov function in the relaxation to equilibrium of a closed (resp. open) system and its variation provides the minimum amount of work needed to manipulate the species concentrations. The theory is used to study analytically the Turing pattern formation in a prototypical reaction-diffusion system, the one-dimensional Brusselator model, and to classify it as a genuine thermodynamic nonequilibrium phase transition. [less ▲] Detailed reference viewed: 11 (0 UL)Response functions as quantifiers of non-Markovianity Strasberg, Philipp ; Esposito, Massimiliano in Physical Review Letters (2018) Quantum non-Markovianity is crucially related to the study of dynamical maps, which are usually derived for initially factorized system-bath states. We here demonstrate that linear response theory also ... [more ▼] Quantum non-Markovianity is crucially related to the study of dynamical maps, which are usually derived for initially factorized system-bath states. We here demonstrate that linear response theory also provides a way to derive dynamical maps, but for initially correlated (and in general entangled) states. Importantly, these maps are always time-translational invariant and allow for a much simpler quantification of non-Markovianity compared to previous approaches. We apply our theory to the Caldeira-Leggett model, for which our quantifier is valid beyond linear response and can be expressed analytically. We find that a classical Brownian particle coupled to an Ohmic bath can already exhibit non-Markovian behaviour, a phenomenon related to the initial state preparation procedure. Furthermore, for a peaked spectral density we demonstrate that there is no monotonic relation between our quantifier and the system-bath coupling strength, the sharpness of the peak or the resonance frequency in the bath. [less ▲] Detailed reference viewed: 9 (0 UL)Detailed Fluctuation Theorems: A Unifying Perspective ; Esposito, Massimiliano in Entropy (2018) We present a general method to identify an arbitrary number of fluctuating quantities which satisfy a detailed fluctuation theorem for all times within the framework of time-inhomogeneous Markovian jump ... [more ▼] We present a general method to identify an arbitrary number of fluctuating quantities which satisfy a detailed fluctuation theorem for all times within the framework of time-inhomogeneous Markovian jump processes. In doing so, we provide a unified perspective on many fluctuation theorems derived in the literature. By complementing the stochastic dynamics with a thermodynamic structure (i.e., using stochastic thermodynamics), we also express these fluctuating quantities in terms of physical observables. [less ▲] Detailed reference viewed: 13 (0 UL)Thermodynamically consistent coarse graining of biocatalysts beyond Michaelis–Menten Wachtel, Artur ; Rao, Riccardo ; Esposito, Massimiliano in New Journal of Physics (2018), 20(4), 042002 Starting from the detailed catalytic mechanism of a biocatalyst we provide a coarse-graining procedure which, by construction, is thermodynamically consistent. This procedure provides stoichiometries ... [more ▼] Starting from the detailed catalytic mechanism of a biocatalyst we provide a coarse-graining procedure which, by construction, is thermodynamically consistent. This procedure provides stoichiometries, reaction fluxes (rate laws), and reaction forces (Gibbs energies of reaction) for the coarse-grained level. It can treat active transporters and molecular machines, and thus extends the applicability of ideas that originated in enzyme kinetics. Our results lay the foundations for systematic studies of the thermodynamics of large-scale biochemical reaction networks. Moreover, we identify the conditions under which a relation between one-way fluxes and forces holds at the coarse-grained level as it holds at the detailed level. In doing so, we clarify the speculations and broad claims made in the literature about such a general flux–force relation. As a further consequence we show that, in contrast to common belief, the second law of thermodynamics does not require the currents and the forces of biochemical reaction networks to be always aligned. [less ▲] Detailed reference viewed: 76 (2 UL)Conservation Laws Shape Dissipation Rao, Riccardo ; Esposito, Massimiliano in New Journal of Physics (2018), 20 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 ... [more ▼] 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. [less ▲] Detailed reference viewed: 63 (7 UL)Quantum thermodynamics of the resonant-level model with driven system-bath coupling Schmidt, Thomas ; Esposito, Massimiliano ; Haughian, Patrick E-print/Working paper (2017) Detailed reference viewed: 65 (6 UL)Fermionic reaction coordinates and their application to an autonomous Maxwell demon in the strong coupling regime Strasberg, Philipp ; ; Schmidt, Thomas et al E-print/Working paper (2017) Detailed reference viewed: 38 (1 UL)Kinetics and thermodynamics of a driven open quantum system Esposito, Massimiliano ; Thingna, Juzar ; in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (2017), 96(5), Detailed reference viewed: 71 (1 UL)Collective effects enhancing power and efficiency ; ; Esposito, Massimiliano in EPL (2017) Energy conversion is most efficient for micro or nano machines with tight coupling between input and output power. To reach meaningful amounts of power, ensembles of N such machines must be considered. We ... [more ▼] Energy conversion is most efficient for micro or nano machines with tight coupling between input and output power. To reach meaningful amounts of power, ensembles of N such machines must be considered. We use a model system to demonstrate that interactions between N tightly coupled nanomachines can enhance the power output per machine. Furthermore, while interactions break tight coupling and thus lower efficiency in finite ensembles, the macroscopic limit (N → ∞) restores it and enhances both the efficiency and the output power per nanomachine. [less ▲] Detailed reference viewed: 8 (0 UL)Carnot efficiency at divergent power output Polettini, Matteo ; Esposito, Massimiliano in Europhysics Letters (2017), 118(40003), The widely debated feasibility of thermodynamic machines achieving Carnot efficiency at finite power has been convincingly dismissed. Yet, the common wisdom that efficiency can only be optimal in the ... [more ▼] The widely debated feasibility of thermodynamic machines achieving Carnot efficiency at finite power has been convincingly dismissed. Yet, the common wisdom that efficiency can only be optimal in the limit of infinitely slow processes overlooks the dual scenario of infinitely fast processes. We corroborate that efficient engines at divergent power output are not theoretically impossible, framing our claims within the theory of Stochastic Thermodynamics. We inspect the case of an electronic quantum dot coupled to three particle reservoirs to illustrate the physical rationale. [less ▲] Detailed reference viewed: 91 (5 UL)Stochastic thermodynamics in the strong coupling regime: An unambiguous approach based on coarse graining Strasberg, Philipp ; Esposito, Massimiliano in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (2017) We consider a classical and possibly driven composite system X ⊗ Y weakly coupled to a Markovian thermal reservoir R so that an unambiguous stochastic thermodynamics ensues for X ⊗ Y . This setup can be ... [more ▼] We consider a classical and possibly driven composite system X ⊗ Y weakly coupled to a Markovian thermal reservoir R so that an unambiguous stochastic thermodynamics ensues for X ⊗ Y . This setup can be equivalently seen as a system X strongly coupled to a non-Markovian reservoir Y ⊗ R. We demonstrate that only in the limit where the dynamics of Y is much faster than X, our unambiguous expressions for thermodynamic quantities, such as heat, entropy, or internal energy, are equivalent to the strong coupling expressions recently obtained in the literature using the Hamiltonian of mean force. By doing so, we also significantly extend these results by formulating them at the level of instantaneous rates and by allowing for time-dependent couplings between X and its environment. Away from the limit where Y evolves much faster than X, previous approaches fail to reproduce the correct results from the original unambiguous formulation, as we illustrate numerically for an underdamped Brownian particle coupled strongly to a non-Markovian reservoir. [less ▲] Detailed reference viewed: 59 (0 UL)Quantum and Information Thermodynamics: A Unifying Framework Based on Repeated Interactions Strasberg, Philipp ; ; et al in Physical Review X (2017), 7(021003), We expand the standard thermodynamic framework of a system coupled to a thermal reservoir by considering a stream of independently prepared units repeatedly put into contact with the system. These units ... [more ▼] We expand the standard thermodynamic framework of a system coupled to a thermal reservoir by considering a stream of independently prepared units repeatedly put into contact with the system. These units can be in any nonequilibrium state and interact with the system with an arbitrary strength and duration. We show that this stream constitutes an effective resource of nonequilibrium free energy, and we identify the conditions under which it behaves as a heat, work, or information reservoir. We also show that this setup provides a natural framework to analyze information erasure (“Landauer’s principle”) and feedback-controlled systems (“Maxwell’s demon”). In the limit of a short system-unit interaction time, we further demonstrate that this setup can be used to provide a thermodynamically sound interpretation to many effective master equations. We discuss how nonautonomously driven systems, micromasers, lasing without inversion and the electronic Maxwell demon can be thermodynamically analyzed within our framework. While the present framework accounts for quantum features (e.g., squeezing, entanglement, coherence), we also show that quantum resources do not offer any advantage compared to classical ones in terms of the maximum extractable work. [less ▲] Detailed reference viewed: 60 (1 UL)Overdamped stochastic thermodynamics with multiple reservoirs ; Esposito, Massimiliano in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (2016), 94(062148), After establishing stochastic thermodynamics for underdamped Langevin systems in contact with multiple reservoirs, we derive its overdamped limit using timescale separation techniques. The overdamped ... [more ▼] After establishing stochastic thermodynamics for underdamped Langevin systems in contact with multiple reservoirs, we derive its overdamped limit using timescale separation techniques. The overdamped theory is different from the naive theory that one obtains when starting from overdamped Langevin or Fokker-Planck dynamics and only coincides with it in the presence of a single reservoir. The reason is that the coarse-grained fast momentum dynamics reaches a nonequilibrium state, which conducts heat in the presence of multiple reservoirs. The underdamped and overdamped theory are both shown to satisfy fundamental fluctuation theorems. Their predictions for the heat statistics are derived analytically for a Brownian particle on a ring in contact with two reservoirs and subjected to a nonconservative force and are shown to coincide in the long-time limit. [less ▲] Detailed reference viewed: 70 (4 UL)Nonequilibrium Thermodynamics of Chemical Reaction Networks: Wisdom from Stochastic Thermodynamics Rao, Riccardo ; Esposito, Massimiliano in Physical Review X (2016), 6(4), 041064 We build a rigorous nonequilibrium thermodynamic description for open chemical reaction networks of elementary reactions. Their dynamics is described by deterministic rate equations with mass action ... [more ▼] We build a rigorous nonequilibrium thermodynamic description for open chemical reaction networks of elementary reactions. Their dynamics is described by deterministic rate equations with mass action kinetics. Our most general framework considers open networks driven by time-dependent chemostats. The energy and entropy balances are established and a nonequilibrium Gibbs free energy is introduced. The difference between this latter and its equilibrium form represents the minimal work done by the chemostats to bring the network to its nonequilibrium state. It is minimized in nondriven detailed-balanced networks (i.e., networks that relax to equilibrium states) and has an interesting information-theoretic interpretation. We further show that the entropy production of complex-balanced networks (i.e., networks that relax to special kinds of nonequilibrium steady states) splits into two non-negative contributions: one characterizing the dissipation of the nonequilibrium steady state and the other the transients due to relaxation and driving. Our theory lays the path to study time-dependent energy and information transduction in biochemical networks. [less ▲] Detailed reference viewed: 174 (23 UL)Conservation laws and symmetries in stochastic thermodynamics Polettini, Matteo ; Bulnes Cuetara, Gregory ; Esposito, Massimiliano in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (2016), 94(052117), Phenomenological nonequilibrium thermodynamics describes how fluxes of conserved quantities, such as matter, energy, and charge, flow from outer reservoirs across a system and how they irreversibly ... [more ▼] Phenomenological nonequilibrium thermodynamics describes how fluxes of conserved quantities, such as matter, energy, and charge, flow from outer reservoirs across a system and how they irreversibly degrade from one form to another. Stochastic thermodynamics is formulated in terms of probability fluxes circulating in the system’s configuration space. The consistency of the two frameworks is granted by the condition of local detailed balance, which specifies the amount of physical quantities exchanged with the reservoirs during single transitions between configurations. We demonstrate that the topology of the configuration space crucially determines the number of independent thermodynamic affinities (forces) that the reservoirs generate across the system and provides a general algorithm that produces the fundamental affinities and their conjugate currents contributing to the total dissipation, based on the interplay between macroscopic conservations laws for the currents and microscopic symmetries of the affinities. [less ▲] Detailed reference viewed: 150 (6 UL)Tightening the uncertainty principle for stochastic currents Polettini, Matteo ; Lazarescu, Alexandre ; Esposito, Massimiliano in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (2016), 94(052104), We connect two recent advances in the stochastic analysis of nonequilibrium systems: the (loose) uncertainty principle for the currents, which states that statistical errors are bounded by thermodynamic ... [more ▼] We connect two recent advances in the stochastic analysis of nonequilibrium systems: the (loose) uncertainty principle for the currents, which states that statistical errors are bounded by thermodynamic dissipation, and the analysis of thermodynamic consistency of the currents in the light of symmetries. Employing the large deviation techniques presented by Gingrich et al. [Phys. Rev. Lett. 116, 120601 (2016)] and Pietzonka, Barato, and Seifert [Phys. Rev. E 93, 052145 (2016)], we provide a short proof of the loose uncertainty principle, and prove a tighter uncertainty relation for a class of thermodynamically consistent currents J . Our bound involves a measure of partial entropy production, that we interpret as the least amount of entropy that a system sustaining current J can possibly produce, at a given steady state. We provide a complete mathematical discussion of quadratic bounds which allows one to determine which are optimal, and finally we argue that the relationship for the Fano factor of the entropy production rate var σ/mean σ 2 is the most significant realization of the loose bound. We base our analysis both on the formalism of diffusions, and of Markov jump processes in the light of Schnakenberg’s cycle analysis. [less ▲] Detailed reference viewed: 99 (3 UL)Fluctuation-Dissipation Relations Far from Equilibrium Altaner, Bernhard ; Polettini, Matteo ; Esposito, Massimiliano in Physical Review Letters (2016), 117(180601), Near equilibrium, where all currents of a system vanish on average, the fluctuation-dissipation relation (FDR) connects a current’s spontaneous fluctuations with its response to perturbations of the ... [more ▼] Near equilibrium, where all currents of a system vanish on average, the fluctuation-dissipation relation (FDR) connects a current’s spontaneous fluctuations with its response to perturbations of the conjugate thermodynamic force. Out of equilibrium, fluctuation-response relations generally involve additional nondissipative contributions. Here, in the framework of stochastic thermodynamics, we show that an equilibriumlike FDR holds for internally equilibrated currents, if the perturbing conjugate force only affects the microscopic transitions that contribute to the current. We discuss the physical requirements for the validity of our result and apply it to nanosized electronic devices. [less ▲] Detailed reference viewed: 190 (9 UL)Work producing reservoirs: Stochastic thermodynamics with generalized Gibbs ensembles ; Esposito, Massimiliano in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (2016), 94(020102), We develop a consistent stochastic thermodynamics for environments composed of thermodynamic reservoirs in an external conservative force field, that is, environments described by the generalized or Gibbs ... [more ▼] We develop a consistent stochastic thermodynamics for environments composed of thermodynamic reservoirs in an external conservative force field, that is, environments described by the generalized or Gibbs canonical ensemble. We demonstrate that small systems weakly coupled to such reservoirs exchange both heat and work by verifying a local detailed balance relation for the induced stochastic dynamics. Based on this analysis, we help to rationalize the observation that nonthermal reservoirs can increase the efficiency of thermodynamic heat engines. [less ▲] Detailed reference viewed: 52 (2 UL)Dissipation in small systems: Landau-Zener approach ; Esposito, Massimiliano in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (2016), 93(062118), We establish a stochastic thermodynamics for a Fermionic level driven by a time-dependent force and interacting with initially thermalized levels playing the role of a reservoir. The driving induces ... [more ▼] We establish a stochastic thermodynamics for a Fermionic level driven by a time-dependent force and interacting with initially thermalized levels playing the role of a reservoir. The driving induces consecutive avoided crossings between system and reservoir levels described within Landau-Zener theory. We derive the resulting system dynamics and thermodynamics and identify energy, work, heat, entropy, and dissipation. Our theory perfectly reproduces the numerically exact quantum work statistics obtained using a two point measurements approach of the total energy and provides an explicit expression for the dissipation in terms of diabatic transitions. [less ▲] Detailed reference viewed: 54 (3 UL) |
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