Related papers: Time evolution of a small reactive system
Quantifying the interaction between a system of interest and its ambient conditions, the memory effect links the states of two distinct Hamiltonians: one for the target system and one for the environment. In this paper, we propose the…
We consider a reaction-diffusion system which may serve as a model for a ferment catalytic reaction in chemistry. The model consists of a system of reaction diffusion equations with unbounded time dependent coefficients and different…
We deal with a system of two coupled differential equations, describing the evolution of a first order phase transition. In particular, we have two non-linear parabolic equations: the first one is deduced from a balance law for entropy and…
The large-time asymptotics of weak solutions to Maxwell--Stefan diffusion systems for chemically reacting fluids with different molar masses and reversible reactions are investigated. The diffusion matrix of the system is generally neither…
The transition between a regime in which thermodynamic relations apply only to ensembles of small systems coupled to a large environment and a regime in which they can be used to characterize individual macroscopic systems is analyzed in…
Autocatalytic reaction system with a small number of molecules is studied numerically by stochastic particle simulations. A novel state due to fluctuation and discreteness in molecular numbers is found, characterized as extinction of…
The transition probability for time-dependent unitary evolution is invariant under the reversal of protocols just as in the classical Liouvillian dynamics. In this article, we generalize the expression of microscopic reversibility to…
Semiclassical techniques have proven to be a very powerful method to extract physical effects from different quantum theories. Therefore, it is expected that in the near future they will play a very prominent role in the context of quantum…
A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…
First-order nonequilibrium phase transitions observed in active matter, fluid dynamics, biology, climate science, and other systems with irreversible dynamics are challenging to analyze because they cannot be inferred from a simple free…
This paper investigates a new formalism to describe real time evolution of quantum systems at finite temperature. A time correlation function among subsystems will be derived which allows for a probabilistic interpretation. Our derivation…
Chemical reactions involve the movement of charges, and this work presents a mathematical model for describing chemical reactions in electrolytes. The model is developed using an energy variational method that aligns with classical…
This article deals with the issues of global-in-time existence and asymptotic analysis of a fluid-particle interaction model in the so-called bubbling regime. The mixture occupies the physical space $\Omega \subset \mathbb{R}^3$ which may…
We study the quantum dynamics of a time reparametrization invariant system with a vanishing Hamiltonian. The evolution of the physical degrees of freedom of the system is described, both at the classical and at the quantum level, in…
For many real physico-chemical complex systems detailed mechanism includes both reversible and irreversible reactions. Such systems are typical in homogeneous combustion and heterogeneous catalytic oxidation. Most complex enzyme reactions…
Two crucial for the breakdown of the master equation arguments are put forward. The first one is related to the violence of a fundamental requirement to the notion of state (thermodynamical) variable, namely: a state variable is defined…
We study the solutions of Von Neumann's expanding model with reversible processes for an infinite reaction network. We show that, contrary to the irreversible case, the solution space need not be convex in contracting phases (i.e. phases…
We prove two theorems concerning the time evolution in general isolated quantum systems. The theorems are relevant to the issue of the time scale in the approach to equilibrium. The first theorem shows that there can be pathological…
A general quantum adiabatic theorem with and without the time-dependent orthogonalization is proven, which can be applied to understand the origin of activation energies in chemical reactions. Further proofs are also developed for the…
Microreversibility rules the fluctuations of the currents flowing across open systems in nonequilibrium (or equilibrium) steady states. As a consequence, the statistical cumulants of the currents and their response coefficients at arbitrary…