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A new formulation of the Phase Field Crystal model is presented that is consistent with the necessary microscopic independence between the phase field, reflecting the broken symmetry of the phase, and both mass density and elastic…

Stochastic systems often exhibit multiple viable metastable states that are long-lived. Over very long timescales, fluctuations may push the system to transition between them, drastically changing its macroscopic configuration. In realistic…

Based on classical statistical thermodynamics, we develop a theoretical approach that provides new insight into how macroscopic and microscopic physical properties are bridged via crystal lattice for condensed mat- ters. We find that in…

Symmetry-breaking bifurcations, where a flow state with a certain symmetry undergoes a transition to state with a different symmetry, are ubiquitous in fluid mechanics. Much can be understood about the nature of these transitions from…

A stochastic deformation of a thermodynamic symplectic structure is studied. The stochastic deformation procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation…

Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterising stochastic effects in biochemical systems is essential to understand the complex dynamics of living…

A thermodynamic phase transition denotes a drastic change of state of a physical system due to a continuous change of thermodynamic variables, as for instance pressure and temperature. The classical van der Waals equation of state is the…

A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature…

Complex systems are composed of many particles or agents that move and interact with one another. The underlying mathematical framework to model many of these systems must incorporate the spatial transport of particles and their…

Spontaneous breaking of continuous time translation symmetry into a discrete one is related to time crystal formation. While the phenomenon is not possible in the ground state of a time-independent many-body system, it can occur in an…

Ecosystems display a complex spatial organization. Ecologists have long tried to characterize them by looking at how different measures of biodiversity change across spatial scales. Ecological neutral theory has provided simple predictions…

Generative diffusion models have achieved spectacular performance in many areas of machine learning and generative modeling. While the fundamental ideas behind these models come from non-equilibrium physics, variational inference and…

Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to…

The reliability of any day-to-day material is critically dictated by its properties. One factor which governs the behaviour of a material, under a given condition, is the microstructure. Despite the absence of any phase transformation, a…

Thermodynamic conventions suffer from describing dynamical distinctions, especially when the structural and energetic changes induced by localized rare events are insignificant. By using the ensemble theory in the trajectory space, we…

The longstanding question of how stochastic behaviour arises from deterministic Hamiltonian dynamics is of great importance, and any truly holistic theory must be capable of describing this transition. In this review, we introduce the…

We study an ideal-gas-like model where the particles exchange energy stochastically, through energy conserving scattering processes, which take place if and only if at least one of the two particles has energy below a certain energy…

Unlike the classical exponential relaxation law, the widely prevailing universal law with its fractional power-law dependence of susceptibility on frequency cannot be explained in the framework of any intuitively simple physical concept.…

For a single enzyme or molecular motor operating in an aqueous solution of non-equilibrated solute concentrations, a thermodynamic description is developed on the level of an individual trajectory of transitions between states. The concept…

The most important recent results in the theory of phase transitions and quantum effects in quantum anharmonic crystals are presented and discussed. In particular, necessary and sufficient conditions for a phase transition to occur at some…