The same reasoning can also determine the change in entropy of the working substance in the heat engine, such as a gas in a cylinder with a moving piston. If the gas absorbs an incremental amount of heat dQ from a heat accumulator at temperature T and expands reversibly relative to the maximum possible holding pressure P, it performs the maximum work dW = P dV, where dV is the volume change. The internal energy of the gas can also change by an amount dU as it expands. Then by conservation of energy, dQ = dU + P dV. Since the net change in entropy for the system plus reservoir is zero when the maximum work is performed, and the entropy of the tank decreases by an amount of dServoir = −dQ/T, this must be compensated by an increase in the entropy of for the working gas, so that dSsystem + dServoir = 0. For each real-world process, less than the maximum work would be done (e.g., due to friction), so that the actual amount of heat dQ′ absorbed by the heat accumulator would be less than the maximum amount of dQ. For example, the gas could expand freely in a vacuum and not work at all. Therefore, it can be determined that with dQ′ = dQ at maximum work corresponds to a reversible process. Depending on the determination of liability, Shannon`s entropy can be applied to the range of possible remedies. In the case where the means are discrete in nature, the ordinary Shannon entropy formula can be used. However, as remedies are generally continuous,21 it becomes necessary to use differential or continuous entropy [53]: Similar to constant volume, the change in entropy As we have already mentioned, a court decision concerning a first-rate relationship (strict law/obligation) leads either to conclude that the defendant had an obligation (responsible) or not. Less often, a judgment may be made on whether or not an actor has a preponderant relationship (power). Before this judgment, the vagueness in the judgment can again be quantified with Shannon`s entropy: From the second law of thermodynamics, it follows that the entropy of a system that is not isolated can decrease.
For example, an air conditioner can cool the air in a room, thereby reducing the entropy of the air in that system. The heat emitted by the room (the system) that the air conditioner carries and releases into the outside air always contributes more to the entropy of the environment than the decrease in the entropy of the air of this system. Thus, the sum of the entropy of space plus the entropy of the environment increases, in accordance with the second law of thermodynamics. where |jr> is a legal claim, |j~r> is the negation of a right, P(jr) = |a|2 is the probability that a legal claim arises by judgment, P(j~r) = |b|2 is the probability of negation, and |a|2 + |b|2 = 1. Also remember that entropy is in this situation: the concept of entropy in physics dates back to the work of Claude [16] in the mid-nineteenth century to describe a property of heat transfer, ΔQ, from a heat source at a certain temperature, T, to an idealized engine in a so-called reversible process.1 In this situation according to Clausius, the entropy of the system increases by ΔQ/T. Similarly, entropy decreases by such an amount when an idealized engine loses heat ΔQ in a heat sink at temperature T. In other words, when heat enters a thermodynamic system, entropy increases – especially when the system is cold, less so when the system is already hot. These concepts can be extended to the entire legal system. First, divide the legal system into independent legal subsystems (since the law is truly a « homogeneous network, » skip this step.) The entropy of any legal subsystem can in principle be constructed using the common and conditional entropies of individual states within the subsystem.
(Even though the law is a transparent network, at some point the correlations between states are so weak that they can be ignored and the legal system treated as if it were composed of independent subsystems.) The idea of the irreversible process is crucial for the change of entropy in the second law. It seems that the entropy of the universe only increases because of its many potential states. Due to more interactions, the second law of thermodynamics states that there will be more entropy. A probabilistic version of Hohfeld`s scheme [15] can also be developed (Sichelman [59]). Here, instead of legal relations, states can exist through a classical binary bit in probabilistic superpositions, best described by a quantum bit (i.e. qubit). The probabilistic nature of the legal relationship may be the result of a lack of knowledge of the underlying system, or due to an inherent indeterminacy of the system itself before judgment (a form of system measure) or a combination of both.18 Using the qubit formalism, one can specify a probabilistic Hohfeld relation in the following form: Since entropy is a state function, the change in entropy of each process, in which temperature and volume vary, is the same as for a path divided into two stages: constant volume heating and constant temperature expansion. For an ideal gas, the total change in entropy [64] is Boltzmann [18] and later Gibbs [19] generalized his equation to account for the fact that some microstates are more or less likely than others. In this case, weighting is required to account for the variable probability of certain microstates corresponding to a given macro state. In this case, using a known mathematical approximation, we use what is called Gibbs entropy: the entropy of a substance can be measured, although indirectly.
The measurement, known as entropymetry[89], is performed on a closed system (where the number of particles N and volume V are constants) and uses the definition of temperature[90] in terms of entropy, while the energy exchange is limited to heat (d U → d Q {displaystyle dUrightarrow dQ} ). Alternatively, the boundary of the terrain can be used as an approximation to define lawful and illegal uses in order to significantly reduce system-wide entropy and thus the cost of information in the delimitation, interpretation and application of the law. In other words, in Smith`s words [8-10], the limit effectively hides the owner`s (unspecified) interests in land use from legal considerations when investigating the actions of a third party. In order to determine whether a third party has unreasonably interfered with the interests of the owner, rather than examining whether a particular act of the third party has interfered with certain uses of the owner, the law generally assumes that if a third party crosses the line unjustifiably, interference occurs. This assumption saves information costs by using the border as a reliable indicator of actual interference in the specific interests of the owner and third parties. Thus, we can define a state function S called entropy that satisfies d S = δ Q rev T {textstyle dS={frac {delta Q_{text{rev}}}{T}}}.