Relationship between Thermodynamic Driving Force and One-Way Fluxes in Reversible Chemical Reactions

This paper studies a mathematical formalism of nonequilibrium thermodynamics for chemical reaction models with $N$ species, $M$ reactions, and general rate law. We establish a mathematical basis for J. W. Gibbs' macroscopic chemical thermodynamics under G. N. Lewis' kinetic law of entire equilibrium (detailed balance in nonlinear chemistry kinetics). In doing so, the equilibrium thermodynamics is then naturally generalized to nonequilibrium settings without detailed balance. ...

In the framework of irreversible thermodynamics, we study autonomous systems of reaction-diffusion equations to show how the entropy and free energy of an open and irreversible reactor depend on concentrations. To do this, we find a Lyapunov function that depends directly on the eigenvalues and eigenvectors of the linearized problem valid for linear and asymptotically stable systems. By suggesting the role of this Lyapunov function as internal free energy, we were able to ref...

Temperature gradients represent energy sources that can be harvested to generate steady reaction or transport fluxes. Technological developments could lead to the transfer of free energy from heat sources and sinks to chemical systems for the purpose of extraction, thermal batteries, or nonequilibrium synthesis. We present a theoretical study of 1D chemical systems subjected to temperature gradients. A complete theoretical framework describes the behavior of the system indu...

Life is a nonequilibrium phenomenon: metabolism provides a continuous supply of energy that drives nearly all cellular processes. However, very little is known about how much energy different cellular processes use, i.e. their energetic costs. The most direct experimental measurements of these costs involve modulating the activity of cellular processes and determining the resulting changes in energetic fluxes. In this review, we present a flux balance framework to aid in the ...

In this paper we present a self-contained macroscopic description of diffusive systems interacting with boundary reservoirs and under the action of external fields. The approach is based on simple postulates which are suggested by a wide class of microscopic stochastic models where they are satisfied. The description however does not refer in any way to an underlying microscopic dynamics: the only input required are transport coefficients as functions of thermodynamic variabl...

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 fo...

Maintained by environmental fluxes, biological systems are thermodynamic processes that operate far from equilibrium without detailed-balance dynamics. Yet, they often exhibit well defined nonequilibrium steady states (NESSs). More importantly, critical thermodynamic functionality arises directly from transitions among their NESSs, driven by environmental switching. Here, we identify constraints on excess thermodynamic quantities that ride above the NESS housekeeping backgrou...

We investigate nonequilibrium chemical reaction systems from the view point of steady state thermodynamics proposed by Oono and Paniconi [Prog. Theor. Phys. Suppl. 130, 29 (1998)]. The concentrations of some compounds are operated by an external system, so that a transition from a steady state to other steady state takes place. We show that an analogue of Clausius inequality holds macroscopically for the operation processes. This implies that the second law of thermodynamics ...

We propose a generalized free energy potential for active systems, including both stochastic master equations and deterministic nonlinear chemical reaction networks. Our generalized free energy is defined variationally as the "most irreversible" state observable. This variational principle is motivated from several perspectives, including large deviations theory, thermodynamic uncertainty relations, Onsager theory, and information-theoretic optimal transport. In passive syste...

We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity, but population wise with statistical rate laws in their syntheses, degradations, spatial diffusion, individual state transitions, and interactions. Such a formal kinetic system in a small volume $V$, like a single cell, can be rigorously trea...