Related papers: Entropy and Convexity for Nonlinear Partial Differ…
Consistency and stability are two essential ingredients in the design of numerical algorithms for partial differential equations. Robust algorithms can be developed by incorporating nonlinear physical stability principles in their design,…
The resolution of the P vs. NP problem, a cornerstone in computational theory, remains elusive despite extensive exploration through mathematical logic and algorithmic theory. This paper takes a novel approach by integrating information…
A simple and effective approach to thermodynamics is suggested, which solves the major difficulties in the traditional presentation of the subject. The internal energy is introduced from the behavior of deformable bodies, whereas the…
I give a quick overview of some of the theoretical background necessary for using modern non-equilibrium statistical physics to investigate the thermodynamics of computation. I first present some of the necessary concepts from information…
Given the evolution of an arbitrary open quantum system, we formulate a general and unambiguous method to separate the internal energy change of the system into an entropy-related contribution and a part causing no entropy change,…
A common approach to evaluate entropy in quantum systems is to solve a master-Bloch equation to determine density matrix and substitute it in entropy definition. However, this method has been recently understood to lack many energy…
Quantum thermodynamics has emerged as a central field for understanding how energy conversion processes occur in microscopic systems. In these systems, effects such as coherence, entanglement, and non-Markovianity play key roles. In this…
Entropy is a fundamental concept from Thermodynamics and it can be used to study models on context of Creation Cold Dark Matter (CCDM). From conditions on the first ($\dot{S}\geq0$)\footnote{Throughout the present work we will use dots to…
It is well known that entropy production is a proxy to the detection of non-equilibrium, i.e. of the absence of detailed balance; however, due to the global character of this quantity, its knowledge does not allow to identify spatial…
Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a…
Partial differential equations are a convenient way to describe reaction- advection-diffusion processes of signalling models. If only one cell type is present, and tissue dynamics can be neglected, the equations can be solved directly.…
To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime of a system. The statistical distributions which can be obtained out of the mesoscopic description characterizing the behaviour of a…
Entropy is one of the most fundamental quantities in physics. For systems with few degrees of freedom, the value of entropy provides a powerful insight into its microscopic dynamics, such as the number, degeneracy and relative energies of…
Accurate characterization of entropy plays a pivotal role in capturing reversible and irreversible heating in supercapacitors during charging/discharging cycles. However, numerical methods that can faithfully capture entropy variation in…
Fluctuating entropy production is studied for a set of linearly coupled complex fields. The general result is applied to non-equilibrium fluctuating hydrodynamic equations for coarse-grained fields (density, temperature and velocity), in…
Existence of an entropy current with non-negative divergence puts a lot of constraints on the transport coefficients of a fluid, so does the existence of equilibrium. In all the cases we have studied so far we have seen an overlap between…
The linear response to temperature changes is derived for systems with overdamped stochastic dynamics. Holding both in transient and steady state conditions, the results allow to compute nonequilibrium thermal susceptibilities from…
The postulates of thermodynamics were originally formulated for macroscopic systems. They lead to the definition of the entropy, which, for a homogeneous system, is a homogeneous function of order one in the extensive variables and is…
The aim of this work is to analyze the entropy, entropy flux and entropy supply rate of granular fluids within the frameworks of the Boltzmann equation and continuum thermodynamics. It is shown that the entropy inequality for a granular gas…
The possible distinction between inanimate and living matter has been of interest to humanity since thousands of years. Clearly, such a rich question can not be answered in a single manner, and a plethora of approaches naturally do exist.…