The purpose of this paper is to discuss the hypothesis that the second law of thermodynamics and its corollaries are manifestations of microscopic quantum effects of the same nature but more general than those described by the Heisenberg uncertainty principle. This hypothesis is new to physics. Energy is a property of matter that has unified our understanding of physical phenomena. It appears prominently in both mechanical and thermodynamic theories. It is defined by the first law of thermodynamics, and its conservation is one of the keystones of analyses of both microscopic and macroscopic phenomena. Adiabatic availability--the amount of work that can be extracted from a system adiabatically--is also a property of matter but has not been accepted with the same unanimity as energy. Experience, especially with large bodies, indicates that not all the energy of a system is available in the form of work. For a given system, say atoms
The purpose of this paper is to discuss the hypothesis that the second law of thermodynamics and its corollaries are manifestations of microscopic quantum effects of the same nature but more general than those described by the Heisenberg uncertainty principle. This hypothesis is new to physics. Energy is a property of matter that has unified our understanding of physical phenomena. It appears prominently in both mechanical and thermodynamic theories. It is defined by the first law of thermodynamics, and its conservation is one of the keystones of analyses of both microscopic and macroscopic phenomena. Adiabatic availability--the amount of work that can be extracted from a system adiabatically--is also a property of matter but has not been accepted with the same unanimity as energy. Experience, especially with large bodies, indicates that not all the energy of a system is available in the form of work. For a given system, say atoms
The second law of thermodynamics places constraints on state transformations. It applies to systems composed of many particles, however, we are seeing that one can formulate laws of thermodynamics when only a small number of particles are interacting with a heat bath. Is there a second law of thermodynamics in this regime? Here, we find that for processes which are approximately cyclic, the second law for microscopic systems takes on a different form compared to the macroscopic scale, imposing not just one constraint on state transformations, but an entire family of constraints. We find a family of free energies which generalize the traditional one, and show that they can never increase. The ordinary second law relates to one of these, with the remainder imposing additional constraints on thermodynamic transitions. We find three regimes which determine which family of second laws govern state transitions, depending on how cyclic the process is. In one regime one can cause an apparent violation of the usual second law, through a process of embezzling work from a large system which remains arbitrarily close to its original state. These second laws are relevant for small systems, and also apply to individual macroscopic systems interacting via long-range interactions. By making precise the definition of thermal operations, the laws of thermodynamics are unified in this framework, with the first law defining the class of operations, the zeroth law emerging as an equivalence relation between thermal states, and the remaining laws being monotonicity of our generalized free energies.
The second law of thermodynamics for adiabatic operations -- constraints on state transitions in closed systems under external control -- is one of the fundamental principles of thermodynamics. On the other hand, it is recently established that even pure quantum states can represent thermal equilibrium. However, pure quantum states do not satisfy the second law in that they are not passive, i.e., work can be extracted from them if arbitrary unitary operations are allowed. It therefore remains unresolved how quantum mechanics can be reconciled with thermodynamics. Here, based on our key quantum-mechanical notions of thermal equilibrium and adiabatic operations, we address the emergence of the second law for adiabatic operations in the thermodynamics limit. We first introduce infinite-observable macroscopic thermal equilibrium (iMATE); a quantum state, including pure states, is in iMATE if the expectation values of all additive observables agree with their equilibrium values. We also introduce a macroscopic operation as unitary evolution generated by a time-dependent additive Hamiltonian, which is regarded as corresponding to adiabatic operations. Employing these concepts, we show that no extensive work can be extracted from any quantum state in iMATE through any macroscopic operations. Furthermore, we introduce a quantum-mechanical form of entropy density such that it agrees with thermodynamic entropy density for any quantum state in iMATE. We then prove that for any initial state in iMATE, this entropy density cannot be decreased by any macroscopic operations, followed by a time-independent relaxation process. Our theory thus proves two different forms of the second law, by adopting macroscopically reasonable classes of observables, equilibrium states, and operations. We also discuss the time scales of macroscopic operations in these results.
To eliminate exceptions to the second law due to fluctuation phenomena, etc., the following changes are necessary. First we must state the laws of thermodynamics in terms of Gibbsian ensembles rather than of individual systems. Second we must sharpen our conception of the experimental procedure required for producing states of thermodynamic equilibrium. It will not suffice to isolate the system and wait. We must have the positive stirring action of thermal contact with a thermostat. Using the new definition of thermal equilibrium we can place statistical mechanics on a more satisfactory footing by showing that the thermostat experimental procedure leads to the canonical ensemble and maximizes v. Neumann's microscopic entropy. (Details of this proof appear in succeeding paper). Difficulties with his macroscopic definition of entropy are avoided by showing that his original microscopic definition is satisfactory when used in conjunction with a proper operational definition of thermodynamic equilibrium. In conclusion the second law of thermodynamics is derived from quantum statistics on the basis of the microscopic definition of entropy.
Thermodynamics is the science that deals with all the phenomena that involve the transfer of energy, i.e. heat and work. Its development started in 1824 with the efforts of Sadi Carnot to improve the closed-cycle steam engine discovered by James Watt in 1764. In 1850, R. Clausius laid the foundations of the laws of thermodynamics. Soon thereafter a conflict between the second law of Thermodynamics and the laws of mechanics was pointed out by Maxwell in 1871 and was illustrated clearly by what has come to be known as Maxwell’s demon. This conflict was addressed by Brillouin (1949) based on the work of Szilard (1929) and of many others. They all claimed that although the objective state of a system is fully describable by mechanics, classical or quantum, and evolves according to the laws of mechanics, some states of the system as perceived by an observer are subjective and reflect the lack of information the observer has about the actual mechanical state of the system. This point of view is, in effect, the information-theory interpretation of thermodynamics which, currently, is widely accepted. The central point of this paper is to describe the reasons why the information-theory interpretation of thermodynamics is contrary to physical reality. It shows that a logically viable hypothesis which reconciles mechanics with thermodynamics is the existence in nature of physical states that have objective uncertainties broader than those implied in quantum theory as it is traditionally formulated. The consequences of this hypothesis are presented in the Unified Quantum Theory of Mechanics and Thermodynamics, by Hatsopoulos and Gyftopoulos.An initial version of this paper was published inJuly of 2006 in the proceedings of ECOS’06, AghiaPelagia, Crete, Greece.
Abstract Quantum mechanics for describing the behavior of microscopic entities and thermodynamics for describing macroscopic systems exhibit separate time concepts. Whereas many theories of modern physics interpret processes as reversible, in thermodynamics, an expression for irreversibility and the so-called time arrow has been developed: the increase of entropy. The divergence between complete reversibility on the one hand and irreversibility on the other is called the paradox of time. Since more than hundred years many efforts have been devoted to unify the time concepts. So far, the efforts were not successful. In this paper a solution is proposed on the basis of matter-energy equivalence with an energetic distinction between matter and mass. By refraining from interpretations predominant in modern theoretical physics, the first and second laws of thermodynamics can be extended to fundamental laws of nature, which are also valid at quantum level.
To reconstruct thermodynamics based on the microscopic laws is one of the most important unfulfilled goals of statistical physics. Here, we show that the first law and the second law for adiabatic processes are derived from an assumption that "probability distributions of energy in Gibbs states satisfy large deviation", which is widely accepted as a property of thermodynamic equilibrium states. We define an adiabatic transformation as a randomized energy-preserving unitary transformations on the many-body systems and the work storage. As the second law, we show that an adiabatic transformation from a set of Gibbs states to another set of Gibbs states is possible if and only if the regularized von Neumann entropy becomes large. As the first law, we show that the energy loss of the thermodynamic systems during the adiabatic transformation is stored in the work storage as "work," in the following meaning; (i) the energy of the work storage takes certain values macroscopically, in the initial state and the final state. (ii) the entropy of the work storage in the final state is macroscopically equal to the entropy of the initial state. As corollaries, our results give the principle of maximam work and the first law for the isothermal processes.