# The physics and mathematics of the second law of thermodynamics (Physics Reports 310 (1999) 1–96)☆

@article{Lieb1999ThePA, title={The physics and mathematics of the second law of thermodynamics (Physics Reports 310 (1999) 1–96)☆}, author={Elliott H. Lieb and Jakob Yngvason}, journal={Physics Reports}, year={1999}, volume={314}, pages={669-669} }

## 215 Citations

### The Mathematics of the Second Law of Thermodynamics

- Physics
- 2010

The essence of the second law is the ‘entropy principle’ which states that adiabatic processes can be quantified by an entropy function on the space of all equilibrium states, whose increase is a…

### Thermodynamics: The Unique Universal Science

- Physics, EducationEntropy
- 2017

The history of thermodynamics is traced from its classical to its postmodern forms, and a tutorial and didactic exposition of thermodynamic principles as it pertains to some of the deepest secrets of the universe are presented.

### A Pedagogical Approach to Obtain the Combined First and Second Law of Thermodynamics from Classical Statistical Mechanics

- Physics
- 2021

The combined first and second law of thermodynamics for a closed system is written as dE=TdS - PdV, where E is the internal energy, S is the entropy, V is the volume, T is the temperature, and P is…

### Comment on the law of entropy increase in thermodynamics

- Physics
- 2012

A common formulation of the law of increase of entropy, found in textbooks on thermodynamics, states that in a process taking place in a completely isolated system the entropy of the final…

### The entropy concept for non-equilibrium states

- PhysicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2013

The conclusion is that it is generally not possible to find a unique entropy that has all relevant physical properties, but it is shown that one can define two entropy functions, called S− and S+, which, taken together, delimit the range of adiabatic processes that can occur between non-equilibrium states.

### Quantum Mechanics Entropy and a Quantum Version of the H-Theorem

- Physics
- 2012

Entropy is a fundamental concept which emerged along with other ideas during the development of thermodynamics and statistical mechanics Landau and Lifshitz (1978); Lieb and Yngvason (1999). Entropy…

### Unitary Proof of the Second Law of Thermodynamics

- Physics, Mathematics
- 2012

In this chapter, we review how to derive the second law of thermodynamics for systems that obey quantum mechanics at the microscopic level. Starting with the statement of the second law, we derive it…

### On the foundations of thermodynamics

- Physics
- 2007

On the basis of new, concise foundations, this paper establishes the four laws of thermodynamics, the Maxwell relations, and the stability requirements for response func- tions, in a form applicable…

### Entropy and the Second Law of Thermodynamics—The Nonequilibrium Perspective

- PhysicsEntropy
- 2020

An alternative to the Carnot-Clausius approach for introducing entropy and the second law of thermodynamics is outlined that establishes entropy as a nonequilibrium property from the onset. Five…

### New definitions of thermodynamic temperature and entropy not based on the concepts of heat and thermal reservoir

- Chemistry
- 2019

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…

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