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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: 174 (6 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: 217 (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: 161 (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: 265 (9 UL)Dissipation in noisy chemical networks: The role of deficiency Esposito, Massimiliano ; Polettini, Matteo ; Wachtel, Artur in Journal of Chemical Physics (2015), 145(18), 184103 We study the effect of intrinsic noise on the thermodynamic balance of complex chemical networks subtending cellular metabolism and gene regulation. A topological network property called deficiency, known ... [more ▼] We study the effect of intrinsic noise on the thermodynamic balance of complex chemical networks subtending cellular metabolism and gene regulation. A topological network property called deficiency, known to determine the possibility of complex behavior such as multistability and oscillations, is shown to also characterize the entropic balance. In particular, when deficiency is zero the average stochastic dissipation rate equals that of the corresponding deterministic model, where correlations are disregarded. In fact, dissipation can be reduced by the effect of noise, as occurs in a toy model of metabolism that we employ to illustrate our findings. This phenomenon highlights that there is a close interplay between deficiency and the activation of new dissipative pathways at low molecule numbers [less ▲] Detailed reference viewed: 229 (22 UL)Efficiency Statistics at All Times: Carnot Limit at Finite Power Polettini, Matteo ; Verley, Gatien ; Esposito, Massimiliano in Physical Review Letters (2015), 114(5), We derive the statistics of the efficiency under the assumption that thermodynamic fluxes fluctuate with normal law, parametrizing it in terms of time, macroscopic efficiency, and a coupling parameter ... [more ▼] We derive the statistics of the efficiency under the assumption that thermodynamic fluxes fluctuate with normal law, parametrizing it in terms of time, macroscopic efficiency, and a coupling parameter zeta. It has a peculiar behavior: no moments, one sub-, and one super-Carnot maxima corresponding to reverse operating regimes (engine or pump), the most probable efficiency decreasing in time. The limit zeta -> 0 where the Carnot bound can be saturated gives rise to two extreme situations, one where the machine works at its macroscopic efficiency, with Carnot limit corresponding to no entropy production, and one where for a transient time scaling like 1/zeta microscopic fluctuations are enhanced in such a way that the most probable efficiency approaches the Carnot limit at finite entropy production. [less ▲] Detailed reference viewed: 201 (8 UL)Irreversible thermodynamics of open chemical networks. I. Emergent cycles and broken conservation laws Polettini, Matteo ; Esposito, Massimiliano in Journal of Chemical Physics (2014), 141 chemical reaction networks, with special regard to metabolic networks regulating cellular physiology and biochemical functions. We first introduce closed networks “in a box”, whose thermodynamics is ... [more ▼] chemical reaction networks, with special regard to metabolic networks regulating cellular physiology and biochemical functions. We first introduce closed networks “in a box”, whose thermodynamics is subjected to strict physical constraints: the mass-action law, elementarity of processes, and detailed balance. We further digress on the role of solvents and on the seemingly unacknowledged property of network independence of free energy landscapes. We then open the system by assuming that the concentrations of certain substrate species (the chemostats) are fixed, whether because promptly regulated by the environment via contact with reservoirs, or because nearly constant in a time window. As a result, the system is driven out of equilibrium. A rich algebraic and topological structure ensues in the network of internal species: Emergent irreversible cycles are associated with nonvanishing affinities, whose symmetries are dictated by the breakage of conservation laws. These central results are resumed in the relation a + b = sY between the number of fundamental affinities a, that of broken conservation laws b and the number of chemostats sY. We decompose the steady state entropy production rate in terms of fundamental fluxes and affinities in the spirit of Schnakenberg’s theory of network thermodynamics, paving the way for the forthcoming treatment of the linear regime, of efficiency and tight coupling, of free energy transduction, and of thermodynamic constraints for network reconstruction. [less ▲] Detailed reference viewed: 281 (14 UL)Generally covariant state-dependent diffusion Polettini, Matteo in Journal of Statistical Mechanics: Theory and Experiment (2013), (07), Statistical invariance of Wiener increments under SO(n) rotations provides a notion of gauge transformation of state-dependent Brownian motion. We show that the stochastic dynamics of non-gauge-invariant ... [more ▼] Statistical invariance of Wiener increments under SO(n) rotations provides a notion of gauge transformation of state-dependent Brownian motion. We show that the stochastic dynamics of non-gauge-invariant systems is not unambiguously defined. They typically do not relax to equilibrium steady states even in the absence of external forces. Assuming both coordinate covariance and gauge invariance, we derive a second-order Langevin equation with state-dependent diffusion matrix and vanishing environmental forces. It differs from previous proposals but nevertheless incorporates the Einstein relation, a Maxwellian conditional steady state for the velocities, and the equipartition theorem. The overdamping limit leads to a stochastic differential equation in state space that cannot be interpreted as a pure differential (Itō, Stratonovich or other). At odds with the latter interpretations, the corresponding Fokker–Planck equation admits an equilibrium steady state; a detailed comparison with other theories of state-dependent diffusion is carried out. We propose this as a theory of diffusion in a heat bath with varying temperature. Besides equilibrium, a crucial experimental signature is the nonuniform steady spatial distribution. [less ▲] Detailed reference viewed: 135 (4 UL)Nonconvexity of the relative entropy for Markov dynamics: A Fisher information approach Polettini, Matteo ; Esposito, Massimiliano in Physics Review E (2013), 88 We show via counterexamples that relative entropy between the solution of a Markovian master equation and the steady state is not a convex function of time. We thus disprove the hypotheses that a general ... [more ▼] We show via counterexamples that relative entropy between the solution of a Markovian master equation and the steady state is not a convex function of time. We thus disprove the hypotheses that a general evolution principle of thermodynamics based on the decrease of the nonadiabatic entropy production could hold. However, we argue that a large separation of typical decay times is necessary for nonconvex solutions to occur, making concave transients extremely short lived with respect to the main relaxation modes. We describe a general method based on the Fisher information matrix to discriminate between generators that admit nonconvex solutions and those that do not. While initial conditions leading to concave transients are shown to be extremely fine-tuned, by our method we are able to select nonconvex initial conditions that are arbitrarily close to the steady state. Convexity does occur when the system is close to satisfying detailed balance or, more generally, when certain normality conditions of the decay modes are satisfied. Our results circumscribe the range of validity of a conjecture by Maes et al. [ Phys. Rev. Lett. 107 010601 (2011)] regarding monotonicity of the large deviation rate functional for the occupation probability, showing that while the conjecture might hold in the long-time limit, the conditions for Lyapunov's second criterion for stability are not met. [less ▲] Detailed reference viewed: 174 (5 UL)Of dice and men. Subjective priors, gauge invariance, and nonequilibrium thermodynamics Polettini, Matteo Scientific Conference (2013, July) "Ceci n'est pas une pipe" wrote Ren\'e Magritte on what was only the representation of a pipe. Phenomena and their physical descriptions differ, and in particular the laws ruling the former might enjoy ... [more ▼] "Ceci n'est pas une pipe" wrote Ren\'e Magritte on what was only the representation of a pipe. Phenomena and their physical descriptions differ, and in particular the laws ruling the former might enjoy symmetries that have to be spent to attain the latter. So, inertial frames are necessary to draw numbers out of Newtonian mechanics and confront with experiment, but ultimately the laws of mechanics are independent of reference frames. Generalizing work done in Ref. [M. Polettini, EPL 97 (2012) 30003] to continuous systems, we discuss from a foundational point of view how subjectivity in the choice of reference prior probability is a (gauge) symmetry of thermodynamics. In particular, a change of priors corresponds to a change of coordinates. Employing an approach based on the stochastic thermodynamics of continuous state-space diffusion processes, we discuss the difference between thermostatic and thermodynamic observables and show that, while the quantification of entropy depends on priors, the second law of thermodynamics is formulated in terms of invariant quantities, in particular the curvature of the thermodynamic force (gauge potential), which we calculate in a few examples of processes led by different nonequilibrium mechanisms. [less ▲] Detailed reference viewed: 123 (1 UL)Fact-Checking Ziegler’s Maximum Entropy Production Principle beyond the Linear Regime and towards Steady States Polettini, Matteo in Entropy (2013), 15(7), 2570-2584 We challenge claims that the principle of maximum entropy production produces physical phenomenological relations between conjugate currents and forces, even beyond the linear regime, and that currents in ... [more ▼] We challenge claims that the principle of maximum entropy production produces physical phenomenological relations between conjugate currents and forces, even beyond the linear regime, and that currents in networks arrange themselves to maximize entropy production as the system approaches the steady state. In particular: (1) we show that Ziegler’s principle of thermodynamic orthogonality leads to stringent reciprocal relations for higher order response coefficients, and in the framework of stochastic thermodynamics, we exhibit a simple explicit model that does not satisfy them; (2) on a network, enforcing Kirchhoff’s current law, we show that maximization of the entropy production prescribes reciprocal relations between coarse-grained observables, but is not responsible for the onset of the steady state, which is, rather, due to the minimum entropy production principle. [less ▲] Detailed reference viewed: 99 (2 UL)Diffusion in nonuniform temperature and its geometric analog Polettini, Matteo in Physical Review. E : Statistical, Nonlinear, and Soft Matter Physics (2013), 87 We propose a Langevin equation for systems in an environment with nonuniform temperature. At odds with an older proposal, ours admits a locally Maxwellian steady state, local equipartition holds, and for ... [more ▼] We propose a Langevin equation for systems in an environment with nonuniform temperature. At odds with an older proposal, ours admits a locally Maxwellian steady state, local equipartition holds, and for detailed-balanced (reversible) systems statistical and physical entropies coincide. We describe its thermodynamics, which entails a generalized version of the first law and Clausius's characterization of reversibility. Finally, we show that a Brownian particle constrained into a smooth curve behaves according to our equation, as if experiencing nonuniform temperature. [less ▲] Detailed reference viewed: 118 (4 UL)Nonequilibrium thermodynamics as a gauge theory Polettini, Matteo in European Physics Letters (2012), 97(3), 30003 We assume that Markovian dynamics on a finite graph enjoys a gauge symmetry under local scalings of the probability density, derive the transformation law for the transition rates and interpret the ... [more ▼] We assume that Markovian dynamics on a finite graph enjoys a gauge symmetry under local scalings of the probability density, derive the transformation law for the transition rates and interpret the thermodynamic force as a gauge potential. A widely accepted expression for the total entropy production of a system arises as the simplest gauge-invariant completion of the time derivative of Gibbs's entropy. We show that transition rates can be given a simple physical characterization in terms of locally detailed balanced heat reservoirs. It follows that Clausius's measure of irreversibility along a cyclic transformation is a geometric phase. In this picture, the gauge symmetry arises as the arbitrariness in the choice of a prior probability. Thermostatics depends on the information that is disposable to an observer; thermodynamics does not. [less ▲] Detailed reference viewed: 173 (2 UL)Macroscopic constraints for the minimum entropy production principle Polettini, Matteo in Physical Review. E (2011), 84(5), In an essential and quite general setup, based on networks, we identify Schnakenberg's observables as the constraints that prevent a system from relaxing to equilibrium, showing that, in the linear regime ... [more ▼] In an essential and quite general setup, based on networks, we identify Schnakenberg's observables as the constraints that prevent a system from relaxing to equilibrium, showing that, in the linear regime, steady states satisfy a minimum entropy production principle. The result is applied to master equation systems, opening a new path to a well-known version of the principle regarding invariant states. Moreover, with the aid of a simple example, the principle is shown to conform to Prigogine's original formulation. Finally, we discuss analogies and differences with a recently proposed maximum entropy production principle. [less ▲] Detailed reference viewed: 115 (2 UL) |
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