Constructal Law and Its Corollaries of Extremum Principles for Energy Expenditure and Entropy Production | A. Heitor Reis

It is shown how both the principles of extremum of entropy production, which are often used in the study of complex systems, follow from the maximization of overall system conductivities, under appropriate constraints. In this way, the maximum rate of entropy production (MEP) occurs when all the forces in the system are kept constant. On the other hand, the minimum rate of entropy production (mEP) occurs when all the currents that cross the system are kept constant. A brief discussion on the validity of the application of the mEP and MEP principles in several cases, and in particular to the Earth’s climate is also presented.


In a recent paper [1] Reis showed that both the principles of extremum of entropy production rate, which are often used in the study of complex systems, are corollaries of the Constructal Law. In fact, both follow from the maximization of overall system conductivities, under appropriate constraints. In this way, the maximum rate of entropy production (MEP) occurs when all the forces in the system are kept constant. On the other hand, the minimum rate of entropy production (mEP) occurs when all the currents that cross the system are kept constant.

In this paper it is shown how the so-called principle of “minimum energy expenditure” which is often used as the basis for explaining many morphologic features in biologic systems, and also in inanimate systems, is also a corollary of Bejan’s Constructal Law [2].

Following the general proof some cases namely, the scaling laws of human vascular systems and river basins are discussed as illustrations from the side of life, and inanimate systems, respectively.

Read More

Thermodynamics today | Prof. Adrian Bejan

In this paper I use the example set by Prof. Jan Szargut as point of reference for a brief look at the current state of thermodynamics—the doctrine, its reach and importance. I start with my first encounter with Prof. Jan Szargut in 1979, and I show how his work influenced mine. Next, I review the structure that underpins thermodynamics as a discipline: the laws and the self-standing phenomena that they underpin, and graphic methods that convey these principles. Along the way, I draw attention to a recent trend that is caused by the inflation in scientific publishing due to the internet: the most common mistakes and misconceptions in thermodynamics, and how they are being spread. In sum, this paper is a call to action, to value, improve and defend the science of thermodynamics. Read More

Helping to evolve our planetary abode to greater and better futures

It we stop and look around us today, we will see that the world has gone mad!! Murders are increasing in our beautiful federation, terrorist attacks are occurring all over the world, wars and instability are escalating in neighbouring lands, and one nation has pulled out of dealing resolutely with the common threat of climate destabilization.… Read More