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Equilibrium thermodynamics is combined with Jarzynski's irreversible work theorem to quantify the excess entropy produced by irreversible processes. The resulting rectified form of the second law parallels the first law, in the sense that…
In the first part of this paper, we propose new optimization-based methods for the computation of preferred (dense, sparse, reversible, detailed and complex balanced) linearly conjugate reaction network structures with mass action dynamics.…
Most of the previous studies on the well-known Gray-Scott model view it as an irreversible chemical reaction system. In this paper, we derive a four-species reaction-diffusion system using the energetic variational approach based on the law…
We discuss entropy production in nonequilibrium steady states by focusing on paths obtained by sampling at regular (small) intervals, instead of sampling on each change of the system's state. This allows us to study directly entropy…
New checkable criteria for persistence of chemical reaction networks are proposed, which extend and complement those obtained by the authors in previous work. The new results allow the consideration of reaction rates which are time-varying,…
We present a general framework for the approximation of systems of hyperbolic balance laws. The novelty of the analysis lies in the construction of suitable relaxation systems and the derivation of a delicate estimate on the relative…
Stochastic chemical processes are described by the chemical master equation satisfying the law of mass-action. We first ask whether the dual master equation, which has the same steady state as the chemical master equation, but with inverted…
In light of the dynamical-systems approach to entropy production in repeated quantum measurements, proposed and illustrated in Commun. Math. Phys. 357, 77-123 (2018) [arXiv:1607.00162] and J. Stat. Phys. 182, 44 (2021) [arXiv:2012.03885],…
In this contribution we prove that the entropy of an N-body isolated system can not decrease and the entropy production should be non-negative provided the system possesses an equilibrium state. We define the entropy as a functional of the…
The balancing of chemical equations is a basic problem in chemistry. A commonly employed method is to convert the task to a linear algebra problem, and then solve the null space of the constructed formula matrix. However, in this method,…
There does not exist a general positive correlation between important life-supporting properties and the entropy production rate. The simple reason is that nondissipative and time-symmetric kinetic aspects are also relevant for establishing…
We show for a large class of interacting particle systems that whenever the stationary measure is not reversible for the dynamics, then the mean entropy production in the steady state is strictly positive. This extends to the thermodynamic…
We demonstrate that in the space of distributions operated on by lattice Boltzmann methods that there exists a vicinity of the equilibrium where collisions with entropy balance are possible and, at the same time, there exist an area of…
We study the entropy production rate in systems described by linear Langevin equations, containing mixed even and odd variables under time reversal. Exact formulas are derived for several important quantities in terms only of the means and…
The 2nd law of thermodynamics yields an irreversible increase in entropy until thermal equilibrium is achieved. This irreversible increase is often assumed to require large and complex systems to emerge from the reversible microscopic laws…
Chemical processes in closed systems are poorly controllable since they always relax to equilibrium. Living systems avoid this fate and give rise to a much richer diversity of phenomena by operating under nonequilibrium conditions. Recent…
Detailed balance of a chemical reaction network can be defined in several different ways. Here we investigate the relationship among four types of detailed balance conditions: deterministic, stochastic, local, and zero-order local detailed…
Irreversibility is one of the most intriguing concepts in physics. While microscopic physical laws are perfectly reversible, macroscopic average behavior has a preferred direction of time. According to the second law of thermodynamics, this…
We study the energetics of isothermal ratchets which are driven by a chemical reaction between two states and operate in contact with a single heat bath of constant temperature. We discuss generic aspects of energy transduction such as…
In this paper we review various information-theoretic characterizations of the approach to equilibrium in biological systems. The replicator equation, evolutionary game theory, Markov processes and chemical reaction networks all describe…