• Corpus ID: 119129350

A definition of thermodynamic entropy valid for non-equilibrium states and few-particle systems

  title={A definition of thermodynamic entropy valid for non-equilibrium states and few-particle systems},
  author={Gian Paolo Beretta and Enzo Zanchini},
  journal={arXiv: Mathematical Physics},
From a new rigorous formulation of the general axiomatic foundations of thermodynamics we derive an operational definition of entropy that responds to the emergent need in many technological frameworks to understand and deploy thermodynamic entropy well beyond the traditional realm of equilibrium states of macroscopic systems. The new definition is achieved by avoiding to resort to the traditional concepts of "heat" (which restricts $a$ $priori$ the traditional definitions of entropy to the… 

A Generalized Statement of Highest-Entropy Principle for Stable Equilibrium and Non-Equilibrium in Many-Particle Systems

Among all statements of Second Law, the existence and uniqueness of stable equilibrium, for each given value of energy content and composition of constituents of any system, have been adopted to

Hierarchical Structure of Generalized Thermodynamic and Informational Entropy

The present research aimed at discussing the thermodynamic and informational aspects of entropy concept to propose a unitary perspective of its definitions as an inherent property of any system in

On Equivalence of Nonequilibrium Thermodynamic and Statistical Entropies

It is shown that the number of microstates in the Boltzmann entropy includes all possible microstates of non-zero probabilities even if the system is trapped in a disjoint component of the microstate space.

Fission and Fusion Nuclear Reactions Second Law Analyses Based on Exergy Method

The present research aims at specializing Second Law analyses to characterize balances of properties, and efficiencies of processes, occurring in nuclear reactions. The conceptual schema is

A Method to Derive the Definition of Generalized Entropy from Generalized Exergy for Any State in Many-Particle Systems

A first novelty proposed in the present study is that mechanical energy, determined by pressure and transferred by work interactions, is also characterized by the entropy property.



Rigorous and General Definition of Thermodynamic Entropy

A rigorous logical scheme is presented that provides a generalized definition of entropy free of the usual unnecessary assumptions which constrain the theory to the equilibrium domain and the existence of the fundamental relation for stable equilibrium states is proved.

Removing Heat and Conceptual Loops from the Definition of Entropy

A rigorous and general logical scheme is presented, which provides an operative non-statistical definition of entropy valid also in the nonequilibrium domain and free of the usual conceptual loops

Recent Progress in the Definition of Thermodynamic Entropy

The principal methods for the definition of thermodynamic entropy are discussed with special reference to those developed by Carath\'eodory, the Keenan School, Lieb and Yngvason, and the present

Steepest Entropy Ascent Model for Far-Non-Equilibrium Thermodynamics. Unified Implementation of the Maximum Entropy Production Principle

By suitable reformulations, we cast the mathematical frameworks of several well-known different approaches to the description of non-equilibrium dynamics into a unified formulation valid in all these

Entropy meters and the entropy of non-extensive systems

  • E. LiebJ. Yngvason
  • Physics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2014
The problem of defining the entropy of macroscopic, but unscalable systems, such as gravitating bodies or systems where surface effects are important, can be overcome, in principle, with the aid of an ‘entropy meter’.

Rigorous Axiomatic Definition of Entropy Valid Also for Non‐Equilibrium States

This work outlines the minimal set of definitions and assumptions required to construct the same definition of entropy by the most direct and essential sequence of logical steps.

Thermodynamics: Energy of nonsimple systems and second postulate

SummaryBy means of new definitions of separable system, separable state and energetic process, the first postulate of thermodynamics and the definition of energy are rigorously extended to nonsimple

Fundamental limitations for quantum and nanoscale thermodynamics.

It is found that there are fundamental limitations on work extraction from non-equilibrium states, owing to finite size effects and quantum coherences, which implies that thermodynamical transitions are generically irreversible at this scale.

Resource theory of quantum states out of thermal equilibrium.

It is shown that the free energy of thermodynamics emerges naturally from the resource theory of energy-preserving transformations, provided that a sublinear amount of coherent superposition over energy levels is available, a situation analogous to the sub linear amount of classical communication required for entanglement dilution.

Work extraction and thermodynamics for individual quantum systems.

It is proved that the second law of thermodynamics holds in this framework, and a simple protocol is given to extract the optimal amount of work from the system, equal to its change in free energy.