(2014 - 2017)
The tendency of the entropy of isolated to increase is considered to be directly linked to the direction of the flow of time. This raises the question whether a quantitative relation can be established such that a time interval can be measured by measuring entropy change and vice versa. The existence or absence of such a link also calls for further consideration of the nature of time. Prigogine argued that the true nature of time can only be discovered by investigating this phenomenon using scientific and philosophical methods. If this is true, then ongoing debates in the metaphysics of time and progress in the scientific study of entropy can be brought together to shed light on this fascinating but elusive concept. In this paper, starting from my recent modified definition of entropy change as a non-dimensional measure of energy change, a direct link between entropy and time duration is presented. It draws from steady energy transfer processes such as heat transfer and shows that a measure of time can be found to be associated with a measure of entropy change. In the absence of other driving forces, the passage of time in an isolated system can therefore be tracked with a well calibrated entropy change meter. When other forces are allowed to interfere and there is no external point from which the system can be considered to be isolated, then the measure of time is non-monotonous since an isolated system can be restored to an earlier state of non-equilibrium.
Black holes are objects of significant interest in modern cosmology. From what initially looked like a superficial analogy between black hole mechanics and thermodynamics, a new epistemological framework has emerged according to which far-reaching conclusions about black hole can be reached through thermodynamic analysis. An example of this is the view that the temperature of a black hole is inversely proportional to its mass. This paper raises doubts about the currently accepted connection between black holes and entropy. It does so by first reviewing the principles of thermodynamics and the properties a system must have in order to admit of proper thermodynamic analysis. It is argued that the current view of black holes preclude their distinct classification either as closed or open systems, a fact which has a bearing on the formulation of the First and Second Laws. From a mechanistic view of temperature and heat, combined with my recent work on the physical meaning of classical entropy, I show that the generalized Second Law of black hole thermodynamics is probably in error. The notion of heat transfer (which is central to entropy definition) is not explicit in the black hole energy equation. To address the challenges raised, black hole mechanics must either commit to a phenomenological approach and therefore only invoke thermodynamics in the classical sense or accept a microscopic view of black hole matter in order to readily draw from established results of statistical mechanics. It is argued that a proper connection to classical thermodynamics would lead to the view that the temperature of a black hole increases with its mass, as a result of which a positive specific heat capacity is to be expected, contrary to the prevailing doctrine.
This year marks the 150th anniversary of the concept of entropy, introduced into thermodynamics by Rudolf Clausius. Despite its central role in the mathematical formulation of the Second Law and most of classical thermodynamics, its physical meaning continues to be elusive and confusing. This is particularly the case when one invokes the connection between the classical thermodynamics of a system and the statistical behavior of its constituent microscopic particles.
This paper sketches Clausius approach to its definition and offers a modified mathematical definition that is still in the spirit of Clausius’ derivation. In the modified version, the differential of specific entropy appears as a non-dimensional energy term that captures the invigoration or reduction of microscopic motion upon addition or withdrawal of heat from the system. It is also argued that heat transfer is a better thermodynamic model process to illustrate the concept of entropy instead of the canonical heat engines and refrigerators that are not relevant to new areas of thermodynamics (e.g. thermodynamics of biological systems). In this light, it is emphasized that entropy changes, as invoked in the Second Law, are necessarily related to the non-equilibrium interactions of two or more systems that might have initially been in thermal equilibrium but at different temperatures. The overall direction of entropy increase indicates the direction of naturally occurring heat transfer processes in an isolated system of internally interacting (non-isolated) sub systems.
We discuss the implication of the proposed modification on the interpretation of entropy in statistical thermodynamics as well as the formulation of the most common thermodynamic potentials.