Stochastic thermodynamics of chemical reactions coupled to finite reservoirs: A case study for the Brusselator

Uncovering nonequilibrium from unresolved events

Closely related to the laws of thermodynamics, the detection and quantification of disequilibria are crucial in unraveling the complexities of nature, particularly those beneath observable layers. Theoretical developments in nonequilibrium thermodynamics employ coarse-graining methods to consider a diversity of partial information scenarios that mimic experimental limitations, allowing the inference of properties such as the entropy production rate. A ubiquitous but rather unexplored scenario involves observing events that can possibly arise from many transitions in the underlying Markov process-which we dub multifilar events-as in the cases of exchanges measured at particle reservoirs, hidden Markov models, mixed chemical and mechanical transformations in biological function, composite systems, and more. We relax one of the main assumptions in a previously developed framework, based on first-passage problems, to assess the non-Markovian statistics of multifilar events. By using the asymmetry of event distributions and their waiting times, we put forward model-free tools to detect nonequilibrium behavior and estimate entropy production, while discussing their suitability for different classes of systems and regimes where they provide no new information, evidence of nonequilibrium, a lower bound for entropy production, or even its exact value. The results are illustrated in reference models through analytics and numerics.

Thermodynamics of a minimal interacting heat engine: Comparison between engine designs

Collective effects stemming from many interacting units have attracted remarkable recent interest, not only for their presence in several systems in nature but also for the possibility of being used for the construction of efficient engine setups. Notwithstanding, little is known about the influence of the engine design, and most studies are restricted to the simplest cases (e.g., simultaneous contact with two thermal baths), not necessarily constituting a realistic setup implementation. In order to investigate the design and its influence on the performance, we introduce the collisional also referred as sequential description for a minimal model for interacting heat engines, composed of two coupled nanomachines placed in contact with a distinct thermal reservoir and subjected to a nonequilibrium work source at each stage. Thermodynamic quantities are exactly obtained irrespective of the model details. Distinct kinds of work sources are investigated and the influence of the interaction, temperature, period, and time asymmetry has been undertaken. Results show that a careful design of interaction provides superior performance than the interactionless case, including optimal power outputs and efficiencies at maximum power greater than known bounds or even the system presenting efficiencies close to the ideal (Carnot) limit. As a complementary analysis, we also show that the case of the system simultaneously placed in contact with two thermal reservoirs constitutes a particular case of our framework.

Nonequilibrium fluctuations of chemical reaction networks at criticality: The Schlögl model as paradigmatic case

Chemical reaction networks can undergo nonequilibrium phase transitions upon variation in external control parameters, such as the chemical potential of a species. We investigate the flux in the associated chemostats that is proportional to the entropy production and its critical fluctuations within the Schlögl model. Numerical simulations show that the corresponding diffusion coefficient diverges at the critical point as a function of system size. In the vicinity of the critical point, the diffusion coefficient follows a scaling form. We develop an analytical approach based on the chemical Langevin equation and van Kampen's system size expansion that yields the corresponding exponents in the monostable regime. In the bistable regime, we rely on a two-state approximation in order to analytically describe the critical behavior.

Machine learning at the mesoscale: A computation-dissipation bottleneck

The cost of information processing in physical systems calls for a trade-off between performance and energetic expenditure. Here we formulate and study a computation-dissipation bottleneck in mesoscopic systems used as input-output devices. Using both real data sets and synthetic tasks, we show how nonequilibrium leads to enhanced performance. Our framework sheds light on a crucial compromise between information compression, input-output computation and dynamic irreversibility induced by nonreciprocal interactions.

Universal minimal cost of coherent biochemical oscillations

Biochemical clocks are essential for virtually all living systems. A biochemical clock that is isolated from an external periodic signal and subjected to fluctuations can oscillate coherently only for a finite number of oscillations. Furthermore, such an autonomous clock can oscillate only if it consumes free energy. What is the minimum amount of free-energy consumption required for a certain number of coherent oscillations? We conjecture a universal bound that answers this question. A system that oscillates coherently for N oscillations has a minimal free-energy cost per oscillation of 4π^{2}Nk_{B}T. Our bound is valid for general finite Markov processes, is conjectured based on extensive numerical evidence, is illustrated with numerical simulations of a known model for a biochemical oscillator, and applies to existing experimental data.

Thermodynamics of concentration vs flux control in chemical reaction networks

We investigate the thermodynamic implications of two control mechanisms of open chemical reaction networks. The first controls the concentrations of the species that are exchanged with the surroundings, while the other controls the exchange fluxes. We show that the two mechanisms can be mapped one into the other and that the thermodynamic theories usually developed in the framework of concentration control can be applied to flux control as well. This implies that the thermodynamic potential and the fundamental forces driving chemical reaction networks out of equilibrium can be identified in the same way for both mechanisms. By analyzing the dynamics and thermodynamics of a simple enzymatic model, we also show that while the two mechanisms are equivalent at steady state, the flux control may lead to fundamentally different regimes where systems achieve stationary growth.

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.

Precision and dissipation of a stochastic Turing pattern

Spontaneous pattern formation is a fundamental scientific problem that has received much attention since the seminal theoretical work of Turing on reaction-diffusion systems. In molecular biophysics, this phenomenon often takes place under the influence of large fluctuations. It is then natural to inquire about the precision of such pattern. In particular, spontaneous pattern formation is a nonequilibrium phenomenon, and the relation between the precision of a pattern and the thermodynamic cost associated with it remains largely unexplored. Here, we analyze this relation with a paradigmatic stochastic reaction-diffusion model, i.e., the Brusselator in one spatial dimension. We find that the precision of the pattern is maximized for an intermediate thermodynamic cost, i.e., increasing the thermodynamic cost beyond this value makes the pattern less precise. Even though fluctuations get less pronounced with an increase in thermodynamic cost, we argue that larger fluctuations can also have a positive effect on the precision of the pattern.