Thermokinetic relations.

Thermokinetic relations bound thermodynamic quantities, such as entropy production of a physical system over a certain time interval, with statistics of kinetic (or dynamical) observables, such as mean total variation of the observable over the time interval. We introduce a thermokinetic relation to bound the entropy production or the nonadiabatic (or excess) entropy production for overdamped Markov jump processes, possibly with time-varying rates and nonstationary distributions. For stationary cases, this bound is akin to a thermodynamic uncertainty relation, only involving absolute fluctuations rather than the mean square, thereby offering a better lower bound far from equilibrium. For nonstationary cases, this bound generalizes (classical) speed limits, where the kinetic term is not necessarily the activity (number of jumps) but any trajectory observable of interest. As a consequence, in the task of driving a system from a given probability distribution to another, we find a tradeoff between nonadiabatic entropy production and housekeeping entropy production: the latter can be increased to decrease the former, although to a limited extent. We also find constraints specific to constant-rate Markov processes. We illustrate our thermokinetic relations on simple examples from biophysics and computing devices.

Calcium oscillations optimize the energetic efficiency of mitochondrial metabolism.

Energy transduction is central to living organisms, but the impact of enzyme regulation and signaling on its thermodynamic efficiency is generally overlooked. Here, we analyze the efficiency of ATP production by the tricarboxylic acid cycle and oxidative phosphorylation, which generate most of the chemical energy in eukaryotes. Calcium signaling regulates this pathway and can affect its energetic output, but the concrete energetic impact of this cross-talk remains elusive. Calcium enhances ATP production by activating key enzymes of the tricarboxylic acid cycle while calcium homeostasis is ATP-dependent. We propose a detailed kinetic model describing the calcium-mitochondria cross-talk and analyze it using nonequilibrium thermodynamics: after identifying the effective reactions driving mitochondrial metabolism out of equilibrium, we quantify the mitochondrial thermodynamic efficiency for different conditions. Calcium oscillations, triggered by extracellular stimulation or energy deficiency, boost the thermodynamic efficiency of mitochondrial metabolism, suggesting a compensatory role of calcium signaling in mitochondrial bioenergetics.

Generalized virial equation for nonlinear multiplicative Langevin dynamics: Application to laser-cooled atoms.

The virial theorem, and the equipartition theorem in the case of quadratic degrees of freedom, are handy constraints on the statistics of equilibrium systems. Their violation is instrumental in determining how far from equilibrium a driven system might be. We extend the virial theorem to nonequilibrium conditions for Langevin dynamics with nonlinear friction and multiplicative noise. In particular, we generalize it for confined laser-cooled atoms in the semiclassical regime. The resulting relation between the lowest moments of the atom position and velocity allows to measure in experiments how dissipative the cooling mechanism is. Moreover, its violation can reveal the departure from a strictly harmonic confinement or from the semiclassical regime.

Tight uncertainty relations for cycle currents.

Several recent inequalities bound the precision of a current, i.e., a counter of the net number of transitions in a system, by a thermodynamic measure of dissipation. However, while currents may be defined locally, dissipation is a global property. Inspired by the fact that, ever since Carnot, cycles are the unit elements of thermodynamic processes, we prove similar bounds tailored to cycle currents, counting net cycle completions, in terms of their conjugate affinities. We show that these inequalities are stricter than previous ones, even far from equilibrium, and that they allow us to tighten those on transition currents. We illustrate our results with a simple model and discuss some technical and conceptual issues related to shifting attention from transition to cycle observables.

Local detailed balance across scales: From diffusions to jump processes and beyond.

Diffusive dynamics in presence of deep energy minima and weak nongradient forces can be coarse grained into a mesoscopic jump process over the various basins of attraction. Combining standard weak-noise results with a path integral expansion around equilibrium, we show that the emerging transition rates satisfy local detailed balance (LDB). Namely, the log ratio of the transition rates between nearby basins of attractions equals the free-energy variation appearing at equilibrium, supplemented by the work done by the nonconservative forces along the typical transition path. When the mesoscopic dynamics possesses a large-size deterministic limit, it can be further reduced to a jump process over macroscopic states satisfying LDB. The persistence of LDB under coarse graining of weakly nonequilibrium states is a generic consequence of the fact that only dissipative effects matter close to equilibrium.

Nonequilibrium thermodynamics of non-ideal chemical reaction networks.

All current formulations of nonequilibrium thermodynamics of open chemical reaction networks rely on the assumption of non-interacting species. We develop a general theory that accounts for interactions between chemical species within a mean-field approach using activity coefficients. Thermodynamic consistency requires that rate equations do not obey standard mass-action kinetics but account for the interactions with concentration dependent kinetic constants. Many features of the ideal formulations are recovered. Crucially, the thermodynamic potential and the forces driving non-ideal chemical systems out of equilibrium are identified. Our theory is general and holds for any mean-field expression of the interactions leading to lower bounded free energies.

Dissipation-Time Uncertainty Relation.

We show that the entropy production rate bounds the rate at which physical processes can be performed in stochastic systems far from equilibrium. In particular, we prove the fundamental tradeoff ⟨S[over ˙]_{e}⟩T≥k_{B} between the entropy flow ⟨S[over ˙]_{e}⟩ into the reservoirs and the mean time T to complete any process whose time-reversed is exponentially rarer. This dissipation-time uncertainty relation is a novel form of speed limit: the smaller the dissipation, the larger the time to perform a process.

Chemical cloaking.

Hiding an object in a chemical gradient requires one to suppress the distortions it would naturally cause on it. To do so, we propose a strategy based on coating the object with a chemical reaction-diffusion network which can act as an active cloaking device. By controlling the concentration of some species in its immediate surrounding, the chemical reactions redirect the gradient as if the object was not there. We also show that a substantial fraction of the energy required to cloak can be extracted from the chemical gradient itself.

Strong current response to slow modulation: A metabolic case-study.

We study the current response to periodic driving of a crucial biochemical reaction network, namely, substrate inhibition. We focus on the conversion rate of substrate into product under time-varying metabolic conditions, modeled by a periodic modulation of the product concentration. We find that the system exhibits a strong nonlinear response to small driving frequencies both for the mean time-averaged current and for the fluctuations. For the first, we obtain an analytic formula by coarse-graining the original model to a solvable one. The result is nonperturbative in the modulation amplitude and frequency. We then refine the picture by studying the stochastic dynamics of the full system using a large deviation approach that allows us to show the resonant effect at the level of the time-averaged variance and signal-to-noise ratio. Finally, we discuss how this nonequilibrium effect may play a role in metabolic and synthetic networks.

Thermodynamics of chemical waves.

Chemical waves constitute a known class of dissipative structures emerging in reaction-diffusion systems. They play a crucial role in biology, spreading information rapidly to synchronize and coordinate biological events. We develop a rigorous thermodynamic theory of reaction diffusion systems to characterize chemical waves. Our main result consists of defining the proper thermodynamic potential of the local dynamics as a nonequilibrium free energy density and establishing its balance equation. This enables us to identify the dynamics of the free energy, of the dissipation, and of the work spent to sustain the wave propagation. Two prototypical classes of chemical waves are examined. From a thermodynamic perspective, the first is sustained by relaxation toward equilibrium and the second by nonconservative forces generated by chemostats. We analytically study step-like waves, called wavefronts, using the Fisher-Kolmogorov equation as a representative of the first class and oscillating waves in the Brusselator model as a representative of the second. Given the fundamental role of chemical waves as message carriers in biosystems, our thermodynamic theory constitutes an important step toward an understanding of information transfers and processing in biology.

Information Thermodynamics of Turing Patterns.

We 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.

Microscopic derivation of the hydrodynamics of active-Brownian-particle suspensions.

We derive the hydrodynamic equations of motion for a fluid of active particles described by underdamped Langevin equations that reduce to the active-Brownian-particle model, in the overdamped limit. The contraction into the hydrodynamic description is performed by locally averaging the particle dynamics with the nonequilibrium many-particle probability density, whose formal expression is found in the physically relevant limit of high friction through a multiple-time-scale analysis. This approach permits us to identify the conditions under which self-propulsion can be subsumed into the fluid stress tensor and thus to define systematically and unambiguously the local pressure of the active fluid.

Exact symmetries in the velocity fluctuations of a hot Brownian swimmer.

Symmetries constrain dynamics. We test this fundamental physical principle, experimentally and by molecular dynamics simulations, for a hot Janus swimmer operating far from thermal equilibrium. Our results establish scalar and vectorial steady-state fluctuation theorems and a thermodynamic uncertainty relation that link the fluctuating particle current to its entropy production at an effective temperature. A Markovian minimal model elucidates the underlying nonequilibrium physics.

Thermal response of nonequilibrium RC circuits.

We analyze experimental data obtained from an electrical circuit having components at different temperatures, showing how to predict its response to temperature variations. This illustrates in detail how to utilize a recent linear response theory for nonequilibrium overdamped stochastic systems. To validate these results, we introduce a reweighting procedure that mimics the actual realization of the perturbation and allows extracting the susceptibility of the system from steady-state data. This procedure is closely related to other fluctuation-response relations based on the knowledge of the steady-state probability distribution. As an example, we show that the nonequilibrium heat capacity in general does not correspond to the correlation between the energy of the system and the heat flowing into it. Rather, also nondissipative aspects are relevant in the nonequilibrium fluctuation-response relations.

Interacting Brownian dynamics in a nonequilibrium particle bath.

We set up a mesoscopic theory for interacting Brownian particles embedded in a nonequilibrium environment, starting from the microscopic interacting many-body theory. Using nonequilibrium linear-response theory, we characterize the effective dynamical interactions on the mesoscopic scale and the statistics of the nonequilibrium environmental noise, arising upon integrating out the fast degrees of freedom. As hallmarks of nonequilibrium, the breakdown of the fluctuation-dissipation and action-reaction relations for Brownian degrees of freedom is exemplified with two prototypical models for the environment, namely active Brownian particles and stirred colloids.

Inflow rate, a time-symmetric observable obeying fluctuation relations.

While entropy changes are the usual subject of fluctuation theorems, we seek fluctuation relations involving time-symmetric quantities, namely observables that do not change sign if the trajectories are observed backward in time. We find detailed and integral fluctuation relations for the (time-integrated) difference between entrance rate and escape rate in mesoscopic jump systems. Such inflow rate, which is even under time reversal, represents the discrete-state equivalent of the phase-space contraction rate. Indeed, it becomes minus the divergence of forces in the continuum limit to overdamped diffusion. This establishes a formal connection between reversible deterministic systems and irreversible stochastic ones, confirming that fluctuation theorems are largely independent of the details of the underling dynamics.

Energy repartition for a harmonic chain with local reservoirs.

We exactly analyze the vibrational properties of a chain of harmonic oscillators in contact with local Langevin heat baths. Nonequilibrium steady-state fluctuations are found to be described by a set of mode temperatures, independent of the strengths of both the harmonic interaction and the viscous damping. Energy is equally distributed between the conjugate variables of a given mode but differently among different modes, in a manner which depends exclusively on the bath temperatures and on the boundary conditions. We outline how bath-temperature profiles can be designed to enhance or reduce fluctuations at specific frequencies in the power spectrum of the chain length.