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In this paper we will give a categorical proof of the Radon-Nikodym theorem. We will do this by describing the trivial version of the result on finite probability spaces as a natural isomorphism. We then proceed to Kan extend this…
Based on the covariant underdamped and overdamped Langevin equations with Stratonovich coupling to multiplicative noises and the associated Fokker-Planck equations on Riemannian manifold, we present the first law of stochastic…
Thermodynamical arguments are known to be useful in the construction of physically motivated Lyapunov functionals for nonlinear stability analysis of spatially homogeneous equilibrium steady states in thermodynamically isolated systems.…
The GENERIC structure allows for a unified treatment of different discrete models of hydrodynamics. We first propose a finite volume Lagrangian discretization of the continuum equations of hydrodynamics through the Voronoi tessellation. We…
We study transient work Fluctuation Relations (FRs) for Gaussian stochastic systems generating anomalous diffusion. For this purpose we use a Langevin approach by employing two different types of additive noise: (i) internal noise where the…
We investigate the validity of a zeroth thermodynamic law for non-equilibrium systems. In order to describe the thermodynamics of the glassy systems, it has been introduced an extra parameter, the effective temperature which generalizes the…
The recently established connection between stochastic thermodynamics and fluctuating hydrodynamics is applied to a study of efficiencies in the coupled transport of heat and matter on a small scale. A stochastic model for a mesoscopic cell…
We find that the conditional statistics of temperature difference at fixed values of the locally averaged temperature dissipation rate in turbulent convection become Gaussian in the regime where the mixing dynamics is expected to be driven…
The development of stochastic thermodynamics during the last decades prompted the discovery of novel nonequilibrium relations refining our understanding of the second law in small fluctuating systems and its connection with information…
We show how statistical thermodynamics can be formulated in situations in which thermodynamics applies, while equilibrium statistical mechanics does not. A typical case is, in the words of Landau and Lifshitz, that of partial (or…
This study presents a comprehensive framework for constitutive modeling of a frame-invariant fractional-order approach to nonlocal thermoelasticity in solids. For this purpose, thermodynamic and mechanical balance laws are derived for…
We experimentally demonstrate that highly structured distributions of work emerge during even the simple task of erasing a single bit. These are signatures of a refined suite of time-reversal symmetries in distinct functional classes of…
A paradigm for isothermal, mechanical rectification of stochastic fluctuations is introduced in this paper. The central idea is to transform energy injected by random perturbations into rigid-body rotational kinetic energy. The prototype…
We show that the particles in the Calogero-Sutherland Model obey fractional exclusion statistics as defined by Haldane. We construct anyon number densities and derive the energy distribution function. We show that the partition function…
Earlier we showed that the fine structure of the spectrum of amplitude variations in the results of measurements of the processes of different nature (in other words, the fine structure of the dispersion of results or the pattern of the…
The Fluctuation Theorem describes the probability ratio of observing trajectories that satisfy or violate the second law of thermodynamics. It has been proved in a number of different ways for thermostatted deterministic nonequilibrium…
We study dynamical fluctuations in overdamped diffusion processes driven by time periodic forces. This is done by studying fluctuation functionals (rate functions from large deviation theory), of fluctuations around the non-equilibrium…
Motivated by compartmental analysis in engineering and biophysical systems, we present a variational framework for the nonequilibrium thermodynamics of systems involving both distributed and discrete (finite dimensional) subsystems by…
In this paper, we develop variational integrators for the nonequilibrium thermodynamics of simple closed systems. These integrators are obtained by a discretization of the Lagrangian variational formulation of nonequilibrium thermodynamics…
The fact that a temperature and an entropy may be associated with horizons in semi-classical general relativity has led many to suspect that spacetime has microstructure. If this is indeed the case then its description via Riemannian…