Are Determinism and Entropy Contradictory Concepts in Physics and Computation?

[Pavel]

Hi, I'd appreciate it if somebody would clarify a couple of things for me.

First, it looks like the concept of determinism is not the same in physics and the theory of computation. Physical determinism requires a unique evolution forward AND backward. That is, the information doesn't get lost. You can view it as a film roll: a linear transition between states. In computation, however, determinism seems to imply a unique evolution only forward. That is, there is a unique path from the initial state to the end state, but not backwards. The information can get lost in a deterministic finite state machine as you transition and you can't go back to the initial state. Does that sound right? Why different definitions in two domains?

Second, it sounds like classical physical systems are deterministic (by definition I provided above), although there are some exceptions in Newtonian classical mechanics (e.g. point particles accelerating to infinity under the force of gravity). Now if the classical world is deterministic, how does the concept of entropy come into this, conceptually? I understand that when entropy increases, it means that there are more avaliable states for the system to be in than a 'tick of time' before. But if there is a unique history forward, how much sense does it make to talk about available states? There's only one path forward. It's like saying that with every successive slide of the film roll, there are more possibile slides available to be the next slide. Well, not really. Given the transition rules (physical laws) and the initial state, there's one and only one next slide possible. It sounds like these available states are logical possibilities in some abstract space. What am I missing here? Thanks.

Pavel.

 

[Aaron Barnard]

Regarding your first question, the difference between physical determinism and computational determinism can be attributed to the fact that physical systems are typically much more complex than computational ones. In a physical system, it is possible for information to become lost or obscured over time as the system evolves, while in a computational system, the same transition between states will always produce the same result. This means that the concept of determinism can be applied differently in the two domains, since physical determinism requires the ability to trace back and forth between states, while computational determinism only requires a unique forward evolution.

Regarding your second question, entropy is a measure of the number of ways a given system can be arranged. This means that, for example, if a system is composed of several particles, the number of ways these particles can be arranged increases as entropy increases. This concept is related to determinism because, even though there is a unique path forward, that path can be taken in many different ways. This is what allows for the concept of entropy to make sense, even in a deterministic system.

 

[astrokreng]

I can provide some insights into the concepts of determinism and entropy. In physics, determinism refers to the idea that the future state of a system can be determined by its current state and the laws of nature. This means that if we know the exact initial conditions of a system and the laws governing its behavior, we can predict its future state with 100% accuracy. This concept is often associated with classical mechanics, where the laws of motion and gravity allow us to accurately predict the movements of objects in our everyday world.

In the theory of computation, determinism refers to the idea that for a given input, there is only one possible sequence of steps that a computer program can follow to produce a certain output. This means that the outcome of a computation is predetermined and unambiguous. However, it is important to note that this concept of determinism is not the same as physical determinism. In computation, we are dealing with abstract symbols and algorithms, while in physics we are dealing with physical objects and laws.

The concept of entropy, on the other hand, is related to the amount of disorder or randomness in a system. In classical mechanics, entropy is often associated with the second law of thermodynamics, which states that in a closed system, the total entropy will always increase or remain constant. This means that as time goes on, the system becomes more disordered and less predictable.

So how do these concepts relate to each other? In classical physics, determinism and entropy seem to contradict each other. If the future state of a system is predetermined, then how can it become more disordered over time? This is where the concept of probability comes in. While the laws of physics may be deterministic, the complex interactions and large number of particles involved in a system make it impossible to predict the exact outcome with 100% accuracy. Instead, we use probabilities to describe the likelihood of a certain state occurring.

In computation, the concept of determinism does not necessarily contradict the concept of entropy. While there may be only one possible path from the initial state to the end state, there can still be variations in the input or the exact steps taken to reach the end state. This can lead to different outcomes and potential for disorder or randomness.

In summary, determinism and entropy are complex concepts that may have different definitions and applications in different domains. However, they both play important roles in understanding the behavior and evolution of systems, whether they are physical or computational.