Andrea Di Vita was trained as a plasma physicist, and has been engaged in nuclear fusion research. His work mainly concerns the stability of gas turbine burners against spontaneous, dangerous thermo-acoustic instabilities (AKA 'humming'), which transform combustion energy into mechanical energy and may destroy low-pollution, high-power burners. His primary fields of interest are non-equilibrium thermodynamics and non-linear analysis. He is a Visiting Scientist at the Università degli Studi di Genova, Dipartimento di Ingegneria civile, chimica e ambientale (DICCA).

1 Looking for the Holy Grail?

2 Thermodynamic equilibrium

2.1 Some fundamental concepts

2.2 A minimum amount of work

2.3 Thermodynamic potentials .

2.4 The impact of magnetic field

2.5 A symmetry

3 LTE

3.1 Le Châtelier's principle

3.2 What is LTE and what Le Châtelier's principle says about it

3.3 Some consequences

3.4 The role of gravity

3.4.1 Collapse

3.4.2 Constant gravitational field

3.5 Continuous vs. discontinuous systems

3.6 GEC

4.1 Discontinuous systems

4.1.1 What is LNET

4.1.2 Onsager's symmetry

4.1.3 Rayleigh's dissipation function

4.1.4 MinEP in discontinuous systems

4.1.5 The least dissipation principle

4.1.6 The balance of entropy in a copper wire

4.1.8 Seebeck effect

4.1.9 Peltier effect

4.1.11 Kelvin's thermocouple equations

4.1.12 Knudsen vs. Pascal

4.2 Entropy balance in fluids

4.2.1 Dissipationless fluids

4.2.2 Viscous fluids

4.2.3 Joule-Thomson throttled expansion

4.2.4 Fluids with electromagnetic fields

4.2.5 Fluids with many non-reacting species

4.2.6 Fluids with many species reacting with each other

4.2.7 Fluids with gravity

4.2.8 Local form of the entropy balance

4.2.9 Global form of the entropy balance: back to the copper wire

4.3 Continuous systems

4.3.1 A slight abuse of notation

4.3.2 Thermodynamic forces and fluxes in continuous systems

4.3.3 Entropy production due to diffusion

4.3.4 Saxen's laws

4.3.5 Fick's law

4.3.6 Soret effect and Dufour effect

4.3.7 Entropy production due to reactions among species

4.3.8 Coupling of diffusion and reactions

4.3.9 GEC in fluids with diffusion and reactions

4.3.10 MinEP in continuous systems

5 Beyond LNET

5.1 Gage et al.'s theorem

5.2 Heat conduction

5.2.1 Fourier's law

5.2.2 Stability vs. Fourier's law

5.3 MinEP

5.3.1 Joule heating: Kirchhoff's principle

5.3.2 Electric arc

5.3.4 Back to Ohm

5.3.5 An auxiliary relationship

5.3.6 What if Joule heating is negligible?

5.3.7 Viscosity: Korteweg-Helmholtz' principle

5.3.8 Maximum economy: yardangs, rivers and the human blood

5.3.9 Porous media

5.3.10 Stability vs. Kirchhoff's and Korteweg-Helmholtz' principles

5.3.11 Convection at moderate Ra

5.3.12 Turbulent flow between fixed parallel surfaces

5.4 Bejan's 'constructal law'

5.5 Zipf's principle of least effort

5.5.1 Of words and bells

5.5.2 City air makes you free .

5.5.3 Pareto

5.5.4 A tale of two cities

5.5.5 Travels with entropy

5.6 MEPP

5.6.1 Muffled intuitions

5.6.2 MEPP vs. MinEP

5.6.3 A thought experiment

5.6.5 Two remarkable exceptions

5.6.6 Heat conduction in gases

5.6.7 Convection at large Ra

5.6.8 The H-mode

5.6.9 Shock waves

5.6.10 Dunes

5.6.11 Solids

5.6.12 Earth's oceans and atmosphere

5.7 Lotka and Odum's maximum power principle

5.8 Oscillating relaxed states

5.8.1 Rules of selection

5.8.2 Biwa et al.'s experiment

5.8.3 Meija et al.'s experiment

5.8.4 Hong et al.'s experiment

5.8.5 Holyst et al.'s simulations

5.8.6 Rauschenbach's hypothesis

5.8.7 Rayleigh's criterion of thermoacoustics

5.8.8 Rijke's tube

5.8.9 Sondhauss' tube

5.8.10 Welander's loop

5.8.11 Eddington and the Cepheids

6 A room, a heater and a window

6.1 When principles collide

6.1.1 The problem

6.1.2 Insufficient approaches

6.1.3 Excess entropy production and dissipative structures

6.1.4 Selective decay

6.1.5 Maximal entropy

6.1.6 Extended irreversible thermodynamics

6.1.7 Steepest ascent

6.1.8 Second entropy

6.1.9 Information thermodynamics and MaxEnt

6.1.10 Orthogonality principle

6.1.11 Quasi-thermodynamic approach

6.1.12 Gouy-Stodola's theorem and entropy generation

6.1.13 Much ado for nothing?

6.2.1 A 1st necessary condition for stability

6.2.2 Convection at moderate Ra, retrieved

6.2.3 Two applications of Bejan's constructal law

6.2.4 Kohler's principle

6.2.5 Entropy production in a radiation field

6.2.6 Uniform temperature: a reciprocal problem

6.2.7 ...Joule heating

6.2.8 ...viscous heating

6.2.9 ... and porous media

6.2.10 A 2nd necessary condition for stability

6.2.11 Entropy production of a radiating body

6.2.12 No heater, two windows

6.2.13 Resistors, again

6.2.14 A 2nd necessary condition for stability - general form

6.2.15 Heat conduction in gases, retrieved

6.2.16 Shock waves and dunes, again

6.2.17 Back to entropy generation

6.2.18 Convection, again

6.2.19 Crystal growth, retrieved

6.2.20 Liesegang and gelation

8 Appendices

8.1 Proof of GEC

8.2 Euler-Lagrange equations

8.3 Lagrange multipliers

8.4 Proof of Gage et al.'s theorem