Chemical reaction networks offer a natural nonlinear generalisation of linear Markov jump processes on a finite state-space. In this paper, we analyse the dynamical large deviations of such models, starting from their microscopic version, the chemical master equation. By taking a largevolume limit, we show that those systems can be described by a path integral formalism over a Lagrangian functional of concentrations and chemical fluxes. This Lagrangian is dual to a Hamiltonian, whose trajectories correspond to the most likely evolution of the system given its boundary conditions.The same can be done for a system biased on time-averaged concentrations and currents, yielding a biased Hamiltonian whose trajectories are optimal paths conditioned on those observables. The appropriate boundary conditions turn out to be mixed, so that, in the long time limit, those trajectories converge to well-defined attractors. We are then able to identify the largest value that the Hamiltonian takes over those attractors with the scaled cumulant generating function of our observables, providing a non-linear equivalent to the well-known Donsker-Varadhan formula for jump processes.On that basis, we prove that chemical reaction networks that are deterministically multistable generically undergo first-order dynamical phase transitions in the vicinity of zero bias. We illustrate that fact through a simple bistable model called the Schlögl model, as well as multistable and unstable generalisations of it, and we make a few surprising observations regarding the stability of deterministic fixed points, and the breaking of ergodicity in the large-volume limit. arXiv:1902.08416v1 [cond-mat.stat-mech]

Reaction currents in chemical networks usually increase when increasing their driving affinities. But far from equilibrium the opposite can also happen. We find that such negative differential response (NDR) occurs in reaction schemes of major biological relevance, namely, substrate inhibition and autocatalysis. We do so by deriving the full counting statistics of two minimal representative models using large deviation methods. We argue that NDR implies the existence of optimal affinities that maximize the robustness against environmental and intrinsic noise at intermediate values of dissipation. An analogous behavior is found in dissipative self-assembly, for which we identify the optimal working conditions set by NDR.[3]. Close to equilibrium, such response is severely constrained [4].Since currents are proportional to affinities,  á ñ = J R , the response R must be positive to ensure positivity of the entropy production 1    S = á ñ = J R 0 2 . Far from equilibrium, instead, á ñ J need not be linear in  thus making R not only dependent on the entropy production. Kinetic aspects become relevant [5], thus opening the way to regimes of negative differential response (NDR) [6]. This counterintuitive, yet common phenomenon has been found in a wealth of physical systems after its first discovery in low-temperature semiconductors [7]. Examples are particles in crowded and glassy environments [8][9][10][11][12], tracers in external flows [13,14], hopping processes in disordered media [15,16], molecular motors [17,18], polymer electrophoresis in gels [19], quantum spin chains [20], graphene and thermal transistors [21,22]. The shared feature underlying all these systems is a trapping mechanism arising by (e.g. energetic, geometric, topological) constraints on the system states [23].Here, we show that NDR plays a key role in open chemical reactions networks [24][25][26]. We show for three paradigmatic models-substrate inhibition, autocatalysis and dissipative self-assembly-how it appears in the average macroscopic behavior as well as in the stochastic regime. While the first two are well described core reaction schemes in living organisms [27,28], the latter is currently drawing the attention of chemists [29,30]. Within the scope of these examples we discuss the role of NDR with respect to environmental and intrinsic noise [31][32][33][34]. We first show that the region of marginal stability, i.e. where R;0, ensures robustness against external perturbations (in the affinity) at moderate values of dissipation. We then argue that those systems affected by NDR that are not poised in the region of marginal stability, behave so in order to minimize the dispersion of the current. Such precision is found to be achieved at moderate values of dissipation, yet again. Hence, our findings show that the performance of life-supporting processes does not always increase at larger dissipation rates OPEN ACCESS RECEIVED

We provide a stochastic thermodynamic description across scales for N identical units with allto-all interactions that are driven away from equilibrium by different reservoirs and external forces. We start at the microscopic level with Poisson rates describing transitions between many-body states. We then identify an exact coarse graining leading to a mesoscopic description in terms of Poisson transitions between systems occupations. We also study macroscopic fluctuations using the Martin-Siggia-Rose formalism and large deviation theory. In the macroscopic limit (N → ∞), we derive an exact nonlinear (mean-field) rate equation describing the deterministic dynamics of the most likely occupations. Thermodynamic consistency, in particular the detailed fluctuation theorem, is demonstrated across microscopic, mesoscopic and macroscopic scales. The emergent notion of entropy at different scales is also outlined. Macroscopic fluctuations are calculated semianalytically in an out-of-equilibrium Ising model. Our work provides a powerful framework to study thermodynamics of nonequilibrium phase transitions.