Quantization

Entropy quantification can be performed under the assumption that both the position of a particle in space and its level of energy can be defined as corresponding to one among many enumerable states, even if their number is hugely high. This means that, if absolute values of entropy have to be computed, neither energy nor space should be continuous variables, even though entropy changes can be calculated in any case. Remarkably, quantum theory just says that’s the case, because at a very short scale both energy and space seem to behave like discrete quantities rather than as continuous ones. So, a general string theory, which represents the evolution of quantum theory, appears to be the natural, preferable theoretical framework for the definition of entropy.

The Motional Effector

According to the second law of thermodynamics every spontaneous change, or process, is associated with an increase in entropy. Although the probabilistic distributions of particles and energy give the possible direction of a process, its occurrence is enabled by the motional energy of the particles. Even particles, however, are subjected to constraints of motion that slow down the attainment of some possible changes and thereby reduce their probability of occurrence, especially if alternative pathways to increase entropy are possible and can be accessed faster. Kinetic restraints are therefore key determinants of which processes are activated among the different possible ones.

Distributions of Particles and Energy

The stability of a system is determined by the overall behaviour of the system’s particles. In turn, this behaviour is established on the basis of the natural distributions the particles themselves spontaneously tend to assume. They tend to distribute across space according to a uniform spreading as the most probable outcome, and they also tend to share their energies according to a complex, non-uniform function that is nevertheless probabilistically equilibrated.

From Nature’s Tendency To Statistical Mechanics

Some processes happen spontaneously. What, at a macroscopic level, appears as a nature’s tendency, is an effect of the complex statistical behaviour of the microscopic particles: their overall net effect emerges at the macroscopic level as a spontaneous force that determines if and how a system can spontaneously change, and if and toward which direction a process is therefore started.

More on Reversibility

Once the concept of work has been introduced, the concepts of reversibility, equilibrium, and entropy become clearer and can be better defined. This was the task undertaken by classical mechanics.

Introduction

Basic concepts are defined, such as what thermodynamics aims to, what a system is, which are the state functions that characterize it, what a process is.

The Role of Probability in Defining Entropy

As a probabilistic law, the second law of thermodynamics needs to be conceptualized in terms of the probabilities of events occurring at the microscopic level. This determines the probability of occurrence for macroscopic phenomena. For the best comprehension of this approach, it is necessary to distinguish between “probabilities”, which are subjective predictions of an expected outcome, and “frequencies”, which are objective observations of that outcome. This distinction is of help to unravel some ambiguities in the interpretation of the second law of thermodynamics.

Some Special Instances of Entropy Change

A few particular phenomena are quite difficult to frame into the fundamental equation, nonetheless they can be interpreted to the light of the general idea of statistical mechanics that any system and any overall change tend to the most probable state, i.e., a state that is microscopically equilibrated and then macroscopically stable.

Entropy Increase as Tendency: Drive and Effector

A useful definition of entropy is “a function of the system equilibration, stability, and inertness”, and the tendency to an overall increase of entropy, which is set forth by the second law of thermodynamics, should be meant as “the tendency to the most probable state”, that is, to a state having the highest equilibration, stability, and inertness that the system can reach. The tendency to entropy increase is driven by the probabilistic distributions of matter and energy and it is actualized by particle motion.

Boltzmann Entropy & Equilibrium in Non-Isolated Systems

The microscopic approach of statistical mechanics has developed a series of formal expressions that, depending on the different features of the system and/or process involved, allow for calculating the value of entropy from the microscopic state of the system. This value is maximal when the particles attain the most probable distribution through space and the most equilibrated sharing of energy between them. At the macroscopic level, this means that the system is at equilibrium, a stable condition wherein no net statistical force emerges from the overall behaviour of the particles. If no force is available then no work can be done and the system is inert. This provides the bridge between the probabilistic equilibration that occurs at the microscopic level and the classical observation that, at a macroscopic level, a system is at equilibrium when no work can be done by it.