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

@article{Beretta2014ADO, 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}, year={2014} }

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…

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## References

SHOWING 1-10 OF 38 REFERENCES

### Rigorous and General Definition of Thermodynamic Entropy

- Computer Science
- 2011

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

- Physics
- 2010

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

- MathematicsEntropy
- 2014

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

- Physics
- 2014

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

- PhysicsProceedings 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

- Computer Science
- 2007

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

- Materials Science
- 1992

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.

- PhysicsNature communications
- 2013

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.

- PhysicsPhysical review letters
- 2013

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.

- PhysicsNature communications
- 2014

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.