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Classical phase transitions, like solid-liquid-gas or order-disorder spin magnetic phases, are all driven by thermal energy fluctuations by varying the temperature. On the other hand, quantum phase transitions happen at absolute zero…
In this paper I show that, for a class of reaction networks, the discrete stochastic nature of the reacting species and reactions results in qualitative and quantitative differences between the mean of exact stochastic simulations and the…
The identification and classification of phases in small systems, e.g. nuclei, social and financial networks, clusters, and biological systems, where the traditional definitions of phase transitions are not applicable, is important to…
Properties of nanoparticles have been studied within the framework of Ising model and the method of random-field interactions: the average magnetic moment and position of critical points of the magnetic and the concentration phase…
The development of multicellular organisms proceeds through a series of morphogenetic and cell-state transitions, transforming homogeneous zygotes into complex adults by a process of self-organization. Many of these transitions are achieved…
Autocatalysis underlies the ability of chemical and biochemical systems to replicate. Autocatalysis was recently defined stoichiometrically for reaction networks; five types of minimal autocatalytic networks, termed autocatalytic cores were…
Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in…
Biological systems are notorious for complex behavior within short timescales (e.g. metabolic activity) and longer time scales (e.g. evolutionary selection), along with their complex spatial organization. Because of their complexity and…
Biochemical reaction systems may be viewed as discrete event processes characterized by a number of states and state transitions. These systems may be modeled as state transition systems with transitions representing individual reaction…
Active matter systems comprise self-propelled particles that move on a substrate while leaving chemical trails that influence other particles through chemotaxis (e.g., slime-depositing bacteria). Orientational chemotaxis manifests as a…
The free energies to evacuate the first hydration shell around a solute and a cavity defined by the first hydration shell depend on the system size. This observation interpreted within the quasichemical theory shows that both the…
We study a control system resembling a singularly perturbed system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are…
The article introduces a new relationship between the chemical system complexity and deviation of its bifurcation point from thermodynamic equilibrium. In the formalism of discrete thermodynamics of chemical equilibria, simulation of…
We develop a theory of enzyme catalysis within biological cells where the substrate concentration [S](t) is time dependent, in contrast to the Michaelis-Menten theory that assumes a steady state. We find that the time varying concentration…
Chemical affinities are responsible for driving active matter systems out of equilibrium. At the nano-scale, molecular machines interact with the surrounding environment and are subjected to external forces. The mechano-chemical coupling…
Biochemical reaction networks in living cells usually involve reversible covalent modification of signaling molecules, such as protein phosphorylation. Under conditions of small molecule numbers, as is frequently the case in living cells,…
The behavior of an atomic system is influenced by introducing a metallic surface. This work explores how the decay landscape can be altered by the presence of sharp corners. We examine two scenarios: the modified spontaneous decay of a…
Dense suspensions of fine particles are significant in numerous biological, industrial, and natural phenomena. They also provide an ideal tool to develop statistical mechanics description for out-of-equilibrium systems. Predicting the bulk…
Phase separation drives the formation of biomolecular condensates in cells, which comprise many components and sometimes possess multiple phases. The equilibrium physics of phase separation is well understood, but many components in…
Multistationarity in biological systems is a mechanism of cellular decision making. In particular, signaling pathways regulated by protein phosphorylation display features that facilitate a variety of responses to different biological…