# Clarification on heat propagation

• feynman137
In summary, heat propagation is a deterministic process governed by the diffusion equation, which can be integrated forwards and backwards in time. However, perturbations in the initial conditions can lead to instability in the solution. Temperature itself is a statistical quantity and the heat equation is causal and local in time, meaning that the future state of the system can be determined by its present state and boundary conditions. This does not violate the determinacy and reversibility of classical mechanics.
feynman137
Could you possibly comment the following statement:

'Heat propagation is a semi-deterministic process in that its future is determined by its present but not by its past.'

Is heat propagation a violation of the determinacy and reversibility of the laws of classical mechanics? Thanks

I disagree with the statement. Heat propagation is governed by the diffusion equation, ∇2T = κ ∂T/∂t. This equation is deterministic and can be integrated backwards forwards in time just as easily. The true statement has to do with its stability. When integrating backwards in time, small perturbations will grow and dominate the solution.

Temperature itself is, seen from a fundamental point of view, a statistical quantity. It describes the part of the mean energy of a particle within a many-body system (fluid or solid) which is due to it's irregular motion in the local rest frame of the bulk medium.

The heat equation is, as any physical equation that describes the time evolution of systems, causal, i.e., it describes the evolution of a quantity (or several quantities if you have a coupled set of equations like Maxwell's Equations for electromagnetism), given the history of the quantity (or quantities) at times prior to the time in question. BTW: It is important to note that by definition, time is a directed quantity, i.e., the causality principle defines a "fundamental arrow of time", from which also other "arrows of time" may follow, e.g., the "thermodynamical arrow of time" according to Boltzmann's H theorem.

Very often, and for sure on the fundamental level, the equations are not only causal but even local in time, i.e., one doesn't have to know the whole history of the system prior to the time under consideration, but it is sufficient to know the state of the system at one point in time in the past. That's also true for the heat equation: If you know the temperature field at one point in time and appropriate boundary conditions, it provides a unique solution for the temperature field within the body at any later time.

## 1. What is heat propagation?

Heat propagation is the transfer of thermal energy from one point to another. It occurs through three mechanisms: conduction, convection, and radiation.

## 2. How does heat propagate in different materials?

The way heat propagates depends on the material it is traveling through. In solids, heat is mainly transferred through conduction, where the molecules vibrate and pass energy to each other. In fluids, such as air or water, heat is mainly transferred through convection, where the warmer molecules rise and the cooler ones sink. In vacuum or through transparent materials, heat can be transferred through radiation, where electromagnetic waves carry the energy.

## 3. What factors affect heat propagation?

The rate of heat propagation is affected by several factors, including the temperature difference between the two points, the distance between them, the properties of the material, and the presence of any insulating materials.

## 4. How is heat propagation related to heat transfer?

Heat propagation is a type of heat transfer, along with conduction, convection, and radiation. Heat transfer is the movement of thermal energy from one point to another, and heat propagation is one of the mechanisms by which this transfer can occur.

## 5. Can heat propagation be controlled or manipulated?

Yes, heat propagation can be controlled or manipulated through various methods, such as using insulating materials to slow down the transfer of heat or using reflective surfaces to redirect radiation. Understanding the principles of heat propagation is essential in designing and optimizing thermal systems.

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