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Visuals: The words " walking entropy " zoom out and land on black-and-white footage of a person's legs walking with scratches. A black "streak" wipes part of the footage out, leaving a black line.
- Overview
- Introduction
- Systems and surroundings
- The First Law of Thermodynamics
- The Second Law of Thermodynamics
- Heat increases the randomness of the universe
- Entropy and the Second Law of Thermodynamics
- Entropy in biological systems
First and Second Laws of Thermodynamics, as they apply to biological systems.
•An open system can exchange both energy and matter with its surroundings. The stovetop example would be an open system, because heat and water vapor can be lost to the air.
•A closed system, on the other hand, can exchange only energy with its surroundings, not matter. If we put a very tightly fitting lid on the pot from the previous example, it would approximate a closed system.
•An isolated system is one that cannot exchange either matter or energy with its surroundings. A perfect isolated system is hard to come by, but an insulated drink cooler with a lid is conceptually similar to a true isolated system. The items inside can exchange energy with each other, which is why the drinks get cold and the ice melts a little, but they exchange very little energy (heat) with the outside environment.
[Why is a cooler sometimes called a "closed" system?]
You, like other organisms, are an open system. Whether you think about it or not, you are constantly exchanging energy and matter with your surroundings. For instance, suppose that you eat a carrot, or lift a bag of laundry onto a table, or simply breathe out and release carbon dioxide into the atmosphere. In each case, you are exchanging energy and matter with your environment.
What kind of system are you: open or closed? As it turns out, this is a physics question, not a philosophical one. You, like all living things, are an open system, meaning that you exchange both matter and energy with your environment. For instance, you take in chemical energy in the form of food, and do work on your surroundings in the form of moving, talking, walking, and breathing.
All of the exchanges of energy that take place inside of you (such as your many metabolic reactions), and between you and your surroundings, can be described by the same laws of physics as energy exchanges between hot and cold objects, or gas molecules, or anything else you might find in a physics textbook. Here, we’ll look at two physical laws – the First and Second Laws of Thermodynamics – and see how they apply to biological systems like you.
Thermodynamics in biology refers to the study of energy transfers that occur in molecules or collections of molecules. When we are discussing thermodynamics, the particular item or collection of items that we’re interested in (which could be something as small as a cell, or as large as an ecosystem) is called the system, while everything that's not included in the system we’ve defined is called the surroundings.
For instance, if you were heating a pot of water on the stove, the system might include the stove, pot, and water, while the surroundings would be everything else: the rest of the kitchen, house, neighborhood, country, planet, galaxy, and universe. The decision of what to define as the system is arbitrary (up to the observer), and depending on what you wanted to study, you could equally well make just the water, or the entire house, part of the system. The system and the surroundings together make up the universe.
There are three types of systems in thermodynamics: open, closed, and isolated.
•An open system can exchange both energy and matter with its surroundings. The stovetop example would be an open system, because heat and water vapor can be lost to the air.
•A closed system, on the other hand, can exchange only energy with its surroundings, not matter. If we put a very tightly fitting lid on the pot from the previous example, it would approximate a closed system.
•An isolated system is one that cannot exchange either matter or energy with its surroundings. A perfect isolated system is hard to come by, but an insulated drink cooler with a lid is conceptually similar to a true isolated system. The items inside can exchange energy with each other, which is why the drinks get cold and the ice melts a little, but they exchange very little energy (heat) with the outside environment.
The first law of thermodynamics thinks big: it deals with the total amount of energy in the universe, and in particular, it states that this total amount does not change. Put another way, the First Law of Thermodynamics states that energy cannot be created or destroyed. It can only change form or be transferred from one object to another.
This law may seem kind of abstract, but if we start to look at examples, we’ll find that transfers and transformations of energy take place around us all the time. For example:
•Light bulbs transform electrical energy into light energy (radiant energy).
•One pool ball hits another, transferring kinetic energy and making the second ball move.
•Plants convert the energy of sunlight (radiant energy) into chemical energy stored in organic molecules.
•You are transforming chemical energy from your last snack into kinetic energy as you walk, breathe, and move your finger to scroll up and down this page.
At first glance, the first law of thermodynamics may seem like great news. If energy is never created or destroyed, that means that energy can just be recycled over and over again, right?
Well…yes and no. Energy cannot be created or destroyed, but it can change from more-useful forms into less-useful forms. As it turns out, in every real-world energy transfer or transformation, some amount of energy is converted to a form that’s unusable (unavailable to do work). In most cases, this unusable energy takes the form of heat.
If heat is not doing work, then what exactly does it do? Heat that doesn’t do work goes towards increasing the randomness (disorder) of the universe. That may seem like a big logic jump, so let’s take a step back and see how it can be the case.
When you have two objects (say, two blocks of the same metal) at different temperatures, your system is relatively organized: the molecules are partitioned by speed, with those in the cooler object moving slowly and those in the hotter object moving quickly. If heat flows from the hotter object into the cooler object (as it will spontaneously), the molecules of the hot object slow down, and the molecules of the cool object speed up, until all the molecules are moving at the same average speed. Now, rather than having a partition of between fast and slow molecules, we simply have one big pool of molecules going about the same speed – a less ordered situation than our starting point.
The degree of randomness or disorder in a system is called its entropy. Since we know that every energy transfer results in the conversion of some energy to an unusable form (such as heat), and since heat that does not do work goes to increase the randomness of the universe, we can state a biology-relevant version of the Second Law of Thermodynamics: every energy transfer that takes place will increase the entropy of the universe and reduce the amount of usable energy available to do work (or, in the most extreme case, leave the overall entropy unchanged). In other words, any process, such as a chemical reaction or set of connected reactions, will proceed in a direction that increases the overall entropy of the universe.
[Click here for some mind-bending implications of the Second Law!]
One implication of the second law of thermodynamics is that in order for a process to happen, it must somehow increase the entropy of the universe. This may immediately raise some questions for you when you think about living organisms such as yourself. After all, aren’t you a pretty ordered collection of matter? Every cell in your body has its own internal organization; the cells are organized into tissues, and the tissues into organs; and your entire body maintains a careful system of transport, exchange, and commerce that keeps you alive. Thus, at first glance, it may not be clear how you, or even a simple bacterium, can represent an increase in the entropy of the universe.
To clarify this, let’s look at the energy exchanges that take place in your body – say, when you are going for a walk. As you contract the muscles of your legs to move your body forward, you are using chemical energy from complex molecules such as glucose and converting it into kinetic energy (and, if you’re walking uphill, potential energy). However, you’re doing this with pretty low efficiency: a large fraction of the energy from your fuel sources is simply transformed into heat. Some of the heat keeps your body warm, but much of it dissipates into the surrounding environment.
This transfer of heat increases the entropy of the surroundings, as does the fact that you’re taking large, complex biomolecules and converting them into a lot of small, simple molecules, such as carbon dioxide and water, as you metabolize fuel to power your walk. This example uses a person in motion, but the same would be true for a person, or any other organism, at rest. The person or organism will maintain some basal rate of metabolic activity, causing the breakdown of complex molecules to smaller and more numerous ones and the release of heat, thus increasing the entropy of the surroundings.
Stated more generally, processes that locally decrease entropy, such as those that build and maintain the highly organized bodies of living things, can indeed take place. However, these local decreases in entropy can occur only with an expenditure of energy, where some of that energy is converted into heat or other non-usable forms. The net effect of the original process (local decrease in entropy) and the energy transfer (increase in entropy of surroundings) is an overall increase in the entropy of the universe.
To sum up, the high degree of organization of living things is maintained by a constant input of energy, and is offset by an increase in the entropy of the surroundings.
[Attribution and references]
Mar 15, 2014 · The concept of walk entropy of a graph has been recently introduced in E. Estrada et al. (2014) [4]. In that paper the authors formulated two conjectures about walk entropies. In the present note we prove the first of these two conjectures and propose a stronger form of it.
- Michele Benzi
- 2014
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Jun 1, 2018 · In other words, the walk entropy is the entropy associated with the probability distribution on the vertex set V (G) that is linearly proportional to the subgraph centrality of the vertices.
- Kyle Kloster, Daniel Král, Blair D. Sullivan
- 2018
The walk entropies are strongly related to the walk regularity of graphs and line-graphs. They are not biased by the graph size and have significantly better correlation with the inverse participation ratio of the eigenmodes of the adjacency matrix than other graph entropies.
Sep 27, 2023 · The walkability index consisted of the connectivity index (intersection density), entropy index (land use degree), FAR (floor area ratio, commercial facilities), and household density.
