The Entropy Balance of an Open System

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Living systems like a bacterial cell are open systems. They are constantly exchanging matter with their environment. Processes within the cell are dependent on energy e.g. to rotate the flagella or to pump out toxic products out of the cell, such processes dissipate energy. If there is no more energy available the functioning of the cell comes to an end. It is therefore essential that the organism takes up energy sources like sugar from the environment to maintain cellular processes. In the light of thermodynamics, the processes of nutrient uptake and intracellular conversion can be associated with the entropy. In the infinitesimal time step $dt$ the organism takes up the entropy $dS_e$ (entropy flux) from the environment in form of energy or matter via flux through the membrane and it dissipates the amount $dS_i$ (entropy production) internally. So in total entropy in the system is

\begin{equation} dS=dS_e + dS_i \end{equation}

The second law of thermodynamics, states that every conversion of energy is associated with dissipation. In other words the entropy of the living system increases due to processes like flagella rotation.

\begin{equation} dS_i \geq 0 \end{equation} The energy dissipated must be replaced by, what Erwin Schrödinger called ‘’negentropy’’ or negative entropy, which for a cell are essentially carbohydrates like sugars.

If the environment provides a continuous flow of negentropy, a state that form the point of view of equilibrium thermodynamics is highly improbable, can be maintained. In a steady state (dS=0) situation the negentropy taken up by an organism equals the entropy produced by the organism.

\begin{equation} dS_e = -dS_i \leq 0 \end{equation}

This state far from equilibrium $dS_i \not =0$ is much more appropriate to describe living systems, than equilibrium thermodynamics.