book_cover_big.gifClassical thermodynamics, the dynamics of Carnot, Clausius, Boltzmann, Gibbs, Joule, Kelvin and Helmholtz, is often also called equilibrium thermodynamics. Indeed, frequently we are alerted that classical thermodynamics holds only for systems that are in equilibrium (or at least close to equilibrium). But why is that? For instance, the First Law of thermodynamics, the conservation of energy, holds for any system you could argue. Certainly this is true. But how about the Second Law, the law of ever increasing entropy? Well here it becomes already a bit trickier since the change in entropy for a given change in the system parameters is defined as:

ΔS = ΔQrev / T

where Qrev stands for the reversible exchanged heat and T is the absolute temperature. Thus the change in entropy between start and end state of a system can only be calculated when designing a reversible path from the beginning to the end. The result of all this is that calculations, as they are done by engineers to determine efficiencies, result is upper limits and actual performances are lower.

 However, there are ways to overcome the entropy problem described above. Important  to realize here is that the system properties that we use to describe a system in thermodynamic terms have some peculiarities. Whereas properties such as volume, mass and energy can easily be calculated for any system regardless whether it is in equilibrium or not, parameters such as pressure, temperature, and as we saw above, entropy, are not so straightforward to define for systems that are not at equilibrium. For example if we take two heat reservoirs at different temperatures and we connect them with a heat conducting rod, heat will flow from the hot reservoir to the cooler one. But the temperature in the rod is not so easily defined and for the system as a whole certainly not. The same is true for liquids where we have a thermal gradient established or where we have a pressure gradient because there is a mass transport going on.

 These kind of problems where already noticed in the early days of thermodynamics. Just in the beginning of the second half of the last century a new chapter was added to thermodynamic theory, namely that of non-equilibrium thermodynamics. Important names connected to this are Prigogine and Onsager, both earned the Nobel price for their work. Key assumption done is that the system is broken down in subsystems such that in the subsystems a condition called “local equilibrium” can be assumed. In such a subsystem the internal states can relax much faster to equilibrium than the change in parameters such as pressure and temperature. In general this approach worked well when the systems were not too far from equilibrium.

 But science moves on and new situations were found where also the approach of Onsager and Prigogine no longer were valid. In a recent article in Scientific American and in other articles by J.M. Rubi it is argued that in many relevant systems such as molecular biology and in nanotechnology systems the conditions can be far from equilibrium and the question arises whether the Second Law will still hold up. It appears that if the description of the system under study is done in a multi-parameter space spun by all the relevant parameters in addition to the spatial coordinates that then non-equilibrium thermodynamics can be applied again. And indeed no reason to get worried, the Second Law still holds up.

 As I mentioned  in previous blogs, the discussion on the Second Law is also today still very lively even 150 years after its discovery and description.

 Further reading:

  1. J.M. Rubi, The Long Arm of the Second Law, Scientific American, 41, Nov 2008
  2. J.M.G. Vilar and J.M. Rubi, Thermodynamics “beyond” Local Equilibrium, Sept 2001 (
  3. J.W. Moore, Physical Chemistry, pp 356, 1978, Longman Group Limited, London, ISBN 0 582 44234 6