Stochastic thermodynamics for a periodically driven single-particle pump

The P-type pumps are a large family of integral membrane transporter ATPases. They are divided into five major types based on substrate specificity, from I to V.
A typical P-type pump has three cytosolic domains: nucleotide-binding (N), phosphorylation (P), and activator (A) domains. These domains are connected to the membrane-spanning helices by short amino acid segments. ATP hydrolysis and covalent phosphoenzyme intermediate formation are crucial parts of the catalytic cycle. At the highly...

V-type pumps are ATP-driven pumps found in the vacuolar membranes of plants, yeast, endosomal and lysosomal membranes of animal cells, plasma membranes of a few specialized eukaryotic cells, and some prokaryotes. They are also known as the V1Vo-ATPase, that couple ATP hydrolysis to transport protons against a concentration gradient.
The peripheral or cytosolic V1 domain with eight subunits is involved in ATP hydrolysis. The integral or transmembrane V0 domain containing at least five subunits...

ATP-driven pumps, also known as transport ATPases, are integral membrane proteins. They have binding sites for ATP located on the membrane's cytosolic side and the ion-conducting domain in the transmembrane region. These pumps use the free energy released from ATP hydrolysis to move the solutes across cell membranes against an electrochemical gradient.
There are four main types of ATP-driven pumps - P-type, V-type, F-type, and ABC transporter. All these pumps are of varying complexities and...

A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.

In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...

The Second Law of Thermodynamics states that entropy, or the amount of disorder in a system, increases each time energy is transferred or transformed. Each energy transfer results in a certain amount of energy that is lost—usually in the form of heat—that increases the disorder of the surroundings. This can also be demonstrated in a classic food web. Herbivores harvest chemical energy from plants and release heat and carbon dioxide into the environment. Carnivores harvest the...