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Hydrodynamic helicity signatures the parity symmetry breaking, chirality, of the flow. Statistical hydrodynamics thus respect chirality, as symmetry breaking and restoration are key to their fundamentals, such as the spectral transfer…
Development of thermodynamic induction up to second order gives a dynamical bifurcation for thermodynamic variables and allows for the prediction and detailed explanation of nonequilibrium phase transitions with associated spontaneous…
How is the irreversibility of a high-dimensional chaotic system controlled by the heterogeneity in the non-reciprocal interactions among its elements? In this paper, we address this question using a stochastic model of random recurrent…
The theoretical description of non-equilibrium Bose--Einstein condensate (BEC) is one of the main challenges in modern statistical physics and kinetics. The non-equilibrium nature of BEC makes it impossible to employ the well-established…
Equilibrium statistical mechanics is intended to link the microscopic dynamics of particles to the thermodynamic laws for macroscopic quantities. However, the modern statistical theory is faced with significant difficulties, as applied to…
Equilibrium statistical mechanics provides a robust framework for characterizing phase transitions in systems whose microsopic dynamics are time-reversible. Efforts to develop and validate theoretical frameworks for time-irreversible,…
In this paper we study the dynamics and ergodic theory of certain economic models which are implicitly defined. We consider 1-dimensional and 2-dimensional overlapping generations models, a cash-in-advance model, heterogeneous markets and a…
The electronic thermoelectric coefficients are analyzed in the vicinity of one and two Anderson localization thresholds in three dimensions. For a single mobility edge, we correct and extend previous studies, and find universal approximants…
We use inverse methods of statistical mechanics to explore trade-offs associated with designing interactions to stabilize self-assembled structures against changes in density or temperature. Specifically, we find isotropic,convex-repulsive…
For studying the thermodynamic properties of systems using statistical mechanics we propose an ensemble that lies in between the familiar canonical and microcanonical ensembles. From a comparative study of these ensembles we conclude that…
In this thesis, we present a comprehensive study of chaos and thermalization of the one-dimensional Bose-Hubbard Model (BHM) within the classical field approximation. Two quantitative measures are compared: the ensemble-averaged Finite-time…
We provide an extended acount of the recent statistical mechanical theory of gauge invariance against operator shifting in quantum many-body systems (arXiv:2509.20494). The gauge transformation is enacted by a shifting superoperator that…
The existence of incompatible measurements, epitomized by Heisenberg's uncertainty principle, is one of the distinctive features of quantum theory. So far, quantum incompatibility has been studied for measurements that test the preparation…
We revisit the Rayleigh--Riabouchinsky paradox in dimensional analysis by making explicit the bridge between thermodynamics and the mechanical interpretation of temperature. Boltzmann's constant $k_B$ acts as a dimensional unifier, leading…
We review the general aspects of the concept of temperature in equilibrium and non-equilibrium statistical mechanics. Although temperature is an old and well-established notion, it still presents controversial facets. After a short…
In geometrothermodynamics (GTD), to study the geometric properties of the equilibrium space three thermodynamic metrics have been proposed so far. These metrics are obtained by using the condition of Legendre invariance and can be computed…
Most natural systems operate far from equilibrium, displaying time-asymmetric, irreversible dynamics characterized by a positive entropy production while exchanging energy and matter with the environment. Although stochastic thermodynamics…
This work deals with the physical system governed by a Hamiltonian operator, in two-dimensional space, of spinless charged particles subject to a perpendicular magnetic field B, coupled with a harmonic potential in the context of…
A thermodynamic device placed outdoors, or a local ecosystem, is subject to a variety of different temperatures given by short-tem (daily) and long-term (seasonal) variations. In the long term a superstatistical description makes sense,…
Stochastic thermodynamics is the field of study relating fluctuations in stochastic systems to thermodynamic quantities. The total entropy production (EP), is central to the thermodynamic classification of systems. Non-equilibrium systems…