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In this paper we develop explicitly the general Statistical Thermodynamics formalism to study of systems restricted to lie on revolution surfaces, particularly we derive the virial state equation of sphere and torus. A model to study the…

Using a simple example of biological macromolecules which are partitioned between bulk solution and membrane, we investigate T.L. Hill's phenomenological nanothermodynamics for small systems. By introducing a {\em systems size dependent}…

We formulate thermodynamics of economic systems in terms of an arbitrary probability distribution for a conserved economic quantity. As in statistical physics, thermodynamic macroeconomic variables emerge as the mean value of microeconomic…

The dynamics of microbial communities is incredibly complex, determined by competition for metabolic substrates and cross-feeding of byproducts. Species in the community grow by harvesting energy from chemical reactions that transform…

These lecture notes present an overview of equilibrium statistical mechanics of classical fluids, with special applications to the structural and thermodynamic properties of systems made of particles interacting via the hard-sphere…

Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…

A statistical approach to the description of the thermodynamic properties of the Fermi particle system occupying a half-space over a plane of finite size in a uniform external field is proposed. The number of particles per unit area is…

Many of the most important processes in cells take place on and across membranes. With the rise of an impressive array of powerful quantitative methods for characterizing these membranes, it is an opportune time to reflect on the structure…

We introduce an approach to partitioning networks into communities that not only determines the best community structure, but also provides a range of characterization techniques to assess how significant that structure is. We study the…

Model biomembrane systems play a crucial role in advancing biomedical research by providing simplified yet effective platforms for exploring complex biological mechanisms. These systems span a wide range of scales, from…

This paper considers membranes of globular structure in the framework of the cell model technique. Coupled micropolar and Brinkman-type equations are used to model the flow of micropolar fluid through a spherical cell, consisting of solid…

Biological membranes and vesicles play a central role in living systems, forming dynamic interfaces that regulate cellular organization and function. Classical descriptions of membrane mechanics that are rooted in equilibrium statistical…

We present a modelling framework for the dynamics of cells structured by the concentration of a micromolecule they contain. We derive general equations for the evolution of the cell population and of the extra-cellular concentration of the…

Descriptions of molecular systems usually refer to two distinct theoretical frameworks. On the one hand the quantum pure state, i.e. the wavefunction, of an isolated system which is determined to calculate molecular properties and to…

Non-equilibrium thermodynamics has long been an area of substantial interest to ecologists because most fundamental biological processes, such as protein synthesis and respiration, are inherently energy-consuming. Microbial communities are…

The deep connection between thermodynamics, computation, and information is now well established both theoretically and experimentally. Here, we extend these ideas to show that thermodynamics also places fundamental constraints on…

We discuss the role coarse-grained models play in the investigation of the structure and thermodynamics of bilayer membranes, and we place them in the context of alternative approaches. Because they reduce the degrees of freedom and employ…

Thermoresponsive microgels are soft colloids that find widespread use as model systems for soft matter physics. Their complex internal architecture, made of a disordered and heterogeneous polymer network, has been so far a major challenge…

Membrane tubulation is a ubiquitous process that occurs both at the plasma membrane and on the membranes of intracellular organelles. These tubulation events are known to be mediated by forces applied on the membrane either due to motor…

The methods of statistical mechanics are applied to two-dimensional foams under macroscopic agitation. A new variable -- the total cell curvature -- is introduced, which plays the role of energy in conventional statistical thermodynamics.…