Related papers: Seeing maximum entropy from the principle of virtu…
In this work, we consider a recently proposed entropy S (called varentropy) defined by a variational relationship dI=beta*(d<x>-<dx>) as a measure of uncertainty of random variable x. By definition, varentropy underlies a generalized…
We review the physical foundations of Landauer's Principle, which relates the loss of information from a computational process to an increase in thermodynamic entropy. Despite the long history of the Principle, its fundamental rationale and…
In this paper, we develop a variational foundation for stochastic thermodynamics of finite-dimensional, continuous-time systems. Requiring the second law (non-negative average total entropy production) systematically yields a consistent…
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…
In recent years we have witnessed a concentrated effort to make sense of thermodynamics for small-scale systems. One of the main difficulties is to capture a suitable notion of work that models realistically the purpose of quantum machines,…
Adaptive systems -- such as a biological organism gaining survival advantage, an autonomous robot executing a functional task, or a motor protein transporting intracellular nutrients -- must model the regularities and stochasticity in their…
The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems, by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and…
We present a general method to determine the entropy current of relativistic matter at local thermodynamic equilibrium in quantum statistical mechanics. Provided that the local equilibrium operator is bounded from below and its lowest lying…
Thermodynamic relations are derived from first principles of mechanics for non-equilibrium processes. Since the key role herein is played by the law of increase of entropy, the latter is analyzed at first. It is shown that its derivation…
Thermodynamics is commonly presented as a theory of macroscopic systems in stable equilibrium, built upon assumptions of extensivity and scaling with system size. In this paper, we present a universal formulation of the elementary…
The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…
We challenge claims that the principle of maximum entropy production produces physical phenomenological relations between conjugate currents and forces, even beyond the linear regime, and that currents in networks arrange themselves to…
I present an unbiased method of mapping particles to distribution functions and vice versa. This method alone defines the canonical formulation of statistical mechanics, since it can be used to derive the principle of maximum entropy in…
In mechanics, common energy principles are based on fixed boundary conditions. However, in bridge engineering structures, it is usually necessary to adjust the boundary conditions to make the structure's internal force reasonable and save…
We present a statistical mechanics description to study the ground state of quantum systems. In this approach, averages for the complete system are calculated over the non-interacting energy levels. Taking different interaction parameter,…
In a previous work (M. Campisi. Stud. Hist. Phil. M. P. 36 (2005) 275-290) we have addressed the mechanical foundations of equilibrium thermodynamics on the basis of the Generalized Helmholtz Theorem. It was found that the volume entropy…
We generalize the second law of thermodynamics in its maximum work formulation for a nonequilibrium initial distribution. It is found that in an isothermal process, the Boltzmann relative entropy (H-function) is not just a Lyapunov function…
Statistical mechanics relies on the complete though probabilistic description of a system in terms of all the microscopic variables. Its object is to derive therefrom static and dynamic properties involving some reduced set of variables.…
Maximum-entropy ensembles are key primitives in statistical mechanics from which thermodynamic properties can be derived. Over the decades, several approaches have been put forward in order to justify from minimal assumptions the use of…
We develop the stochastic approach to thermodynamics based on the stochastic dynamics, which can be discrete (master equation) continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of…