The (physical) concept of entropy is predominantly applied to many-particle systems. We can regard such a system as a many-particle system, whose dynamical variables comprise the positions, momenta, and other variable properties of all particles. It can exhibit, in theory, three types of dynmical behaviours:

1. A low-dimensional regular (i.e., non-chaotic) dynamics, i.e., a fixed-point, periodic or quasiperiodic¹ one. Such dynamics are possible for very low temperatures, e.g., a completely frozen system would correspond to a fixed-point dynamics and simple lattice vibrations would correspond to periodic dynamics. For higher temperatures, however, such dynamics do not correspond to what we observe in reality and simulations.

2. A high-dimensional regular dynamics, i.e., a quasiperiodic¹ dynamics. Such a system could be described as the superposition of many independent periodic processes, each having a different, incommensurable frequency. While these processes need not affect a single particle but could be rather obfuscated, there is no reason why they would not interact at all (for a high temperature and sufficiently many processes). Moreover, it can be argued that high-dimensional quasiperiodicity is practically indistinguishable from chaos.

3. A high-dimensional chaotic dynamics.

So, it makes sense to say that a system that has some entropy (i.e., whose temperature is not close to absolute zero) also exhibits a chaotic dynamics on the microscopic level. But this does not mean that the two are the same. In a multi-particle system, it’s not the mere presence of entropy that we care about but how and when it increases. So, entropy and chaos are as much linked as entropy and temperature or, say, mass and momentum.

Noted that this not really about ergodicity. Complex systems with insurmountable energy barriers (consider spin glasses) can still be chaotic; and quasiperiodic dynamics can be ergodic (consider the example of a single particle moving on a quadratic torus, which is ergodic and quasiperiodic if the components of its momentum are incommensurable, but periodic and not ergodic otherwise).

Finally, note that the information-theoretic concept of entropy is used to characterise dynamical systems and to distinguish between chaos and regularity, but I assume this is not the reason for your question.

The (physical) concept of entropy is predominantly applied to many-particle systems. We can regard such a system as high-dimensional dynamical system, whose dynamical variables comprise the positions, momenta, and other variable properties of all particles. It can exhibit, in theory, three types of dynamical behaviours:

1. A low-dimensional regular (i.e., non-chaotic) dynamics, i.e., a fixed-point, periodic or quasiperiodic¹ one. Such dynamics are possible for very low temperatures, e.g., a completely frozen system would correspond to a fixed-point dynamics and simple lattice vibrations would correspond to periodic dynamics. For higher temperatures, however, such dynamics do not correspond to what we observe in reality and simulations.

2. A high-dimensional regular dynamics, i.e., a quasiperiodic¹ dynamics. Such a system could be described as the superposition of many independent periodic processes, each having a different, incommensurable frequency. While these processes need not affect a single particle but could be rather obfuscated, there is no reason why they would not interact at all (for a high temperature and sufficiently many processes). Moreover, it can be argued that high-dimensional quasiperiodicity is practically indistinguishable from chaos.

3. A high-dimensional chaotic dynamics.

So, it makes sense to say that a system that has some entropy (i.e., whose temperature is not close to absolute zero) also exhibits a chaotic dynamics on the microscopic level. But this does not mean that the two are the same. In a multi-particle system, it’s not the mere presence of entropy that we care about but how and when it increases. So, entropy and chaos are as much linked as entropy and temperature or, say, mass and momentum.

Note that this not really about ergodicity. Complex systems with insurmountable energy barriers (consider spin glasses) can still be chaotic; and quasiperiodic dynamics can be ergodic (consider the example of a single particle moving on a quadratic torus, which is ergodic and quasiperiodic if the components of its momentum are incommensurable, but periodic and not ergodic otherwise).

Finally, note that the information-theoretic concept of entropy is used to characterise dynamical systems and to distinguish between chaos and regularity, but I assume this is not the reason for your question.

The (physical) concept of entropy is predominantly applied to many-particle systems. We can regard such a system as a many-particle system, whose dynamical variables comprise the positions, momenta, and other variable properties of all particles. It can exhibit, in theory, three types of dynmical behaviours:

1. A low-dimensional regular dynamics, i.e., a fixed-point, periodic or quasiperiodic one. Such dynamics are possible for very low temperatures, e.g., a completely frozen system would correspond to a fixed-point dynamics and simple lattice vibrations would correspond to periodic dynamics. For higher temperatures, however, such dynamics do not correspond to what we observe in reality and simulations.

2. A high-dimensional regular dynamics, i.e., a quasiperiodic dynamics. Such a system could be described as the superposition of many independent periodic processes, each having a different, incommensurable frequency. While these processes need not affect a single particle but could be rather obfuscated, there is no reason why they would not interact at all (for a high temperature and sufficiently many processes). Moreover, it can be argued that high-dimensional quasiperiodicity is practically indistinguishable from chaos.

3. A high-dimensional chaotic dynamics.

So, it makes sense to say that a system that has some entropy (i.e., whose temperature is not close to absolute zero) also exhibits a chaotic dynamics on the microscopic level. But this does not mean that the two are the same. In a multi-particle system, it’s not the mere presence of entropy that we care about but how and when it increases. So, entropy and chaos are as much linked as entropy and temperature or, say, mass and momentum.

Noted that this not really about ergodicity. Complex systems with insurmountable energy barriers (consider spin glasses) can still be chaotic; and quasiperiodic dynamics can be ergodic (consider the example of a single particle moving on a quadratic torus, which is ergodic and quasiperiodic if the components of its momentum are incommensurable, but periodic and not ergodic otherwise).

Finally, note that the information-theoretic concept of entropy is used to characterise dynamical systems and to distinguish between chaos and regularity, but I assume this is not the reason for your question.

The (physical) concept of entropy is predominantly applied to many-particle systems. We can regard such a system as a many-particle system, whose dynamical variables comprise the positions, momenta, and other variable properties of all particles. It can exhibit, in theory, three types of dynmical behaviours:

1. A low-dimensional regular (i.e., non-chaotic) dynamics, i.e., a fixed-point, periodic or quasiperiodic¹ one. Such dynamics are possible for very low temperatures, e.g., a completely frozen system would correspond to a fixed-point dynamics and simple lattice vibrations would correspond to periodic dynamics. For higher temperatures, however, such dynamics do not correspond to what we observe in reality and simulations.

2. A high-dimensional regular dynamics, i.e., a quasiperiodic¹ dynamics. Such a system could be described as the superposition of many independent periodic processes, each having a different, incommensurable frequency. While these processes need not affect a single particle but could be rather obfuscated, there is no reason why they would not interact at all (for a high temperature and sufficiently many processes). Moreover, it can be argued that high-dimensional quasiperiodicity is practically indistinguishable from chaos.

3. A high-dimensional chaotic dynamics.

So, it makes sense to say that a system that has some entropy (i.e., whose temperature is not close to absolute zero) also exhibits a chaotic dynamics on the microscopic level. But this does not mean that the two are the same. In a multi-particle system, it’s not the mere presence of entropy that we care about but how and when it increases. So, entropy and chaos are as much linked as entropy and temperature or, say, mass and momentum.

Noted that this not really about ergodicity. Complex systems with insurmountable energy barriers (consider spin glasses) can still be chaotic; and quasiperiodic dynamics can be ergodic (consider the example of a single particle moving on a quadratic torus, which is ergodic and quasiperiodic if the components of its momentum are incommensurable, but periodic and not ergodic otherwise).

Finally, note that the information-theoretic concept of entropy is used to characterise dynamical systems and to distinguish between chaos and regularity, but I assume this is not the reason for your question.