TABLE OF CONTENTSPAGEINTRODUCTIONPurpose, acknowledgments, the two methods of approach and outline of treatment1PART ITHE DEFINITIONS, GENERAL PRELIMINARIES, DEVELOPMENT, CURRENT AND PRECISE STATEMENTS OF THE MATTERS CONSIDEREDSECTION A(1)The "state" of a body and its "change of state"5The two points of view; the microscopic and the macroscopic observer; the micro-state and macro-state or aggregate5The selected and the rejected micro-states; the use of the hypothesis of "elementary chaos"7PLANCK'S fuller description of what constitutes the state of a physical system10(2)Further elucidation of the essential prerequisite, "elementary chaos." Sundry aspects of haphazard11BOLTZMANN'S service to science in this field and his view of what constitute the necessary features of haphazard12BURBURY'S simplification of haphazard necessary and his example of "elementary chaos"15Haphazard as expressed by a system possessing an extraordinary number of degrees of freedom17(3)Settled and unsettled states; distinction between final stage of "elementary chaos" and its preceding stages18Each stage has sufficient haphazard; examples and characteristics of the settled and unsettled stages of "elementary chaos"; all micro-states not equally likely; the assumed state of "chaos" does not eliminate adequate haphazard; two anticipatory remarks19SECTION BCONCERNING THE APPLICATION OF THE CALCULUS OF PROBABILITIES(1)The probability concept, its usefulness in the past, its present necessity, and its universality22Popular objection to its use; Boltzmann's justification of this concept; its usefulness in the past and in other fields; some of its good points; the haphazard features necessary for its use23(2)What is meant by probability of a state? Example27SECTION C(1)The existence, definition, measure, properties, relations and scope of irreversibility and reversibility29Inference from experience; inference from the H-theorem or calculus of probabilities; definitions of irreversible and reversible processes; examples of each30(2)Character of process decided by limiting states32Nature's preference for a state; measure of this preference33Entropy both the criterion and the measure of irreversibility33(3)All the irreversible processes stand or fall together34(4)Convenience of the fiction, the reversible processes35Entropy the only universal measure of irreversibility. Outcome of the whole study of irreversibility36SECTION D(1)The gradual development of the idea that entropy depends on probability or number of complexions37Why it is difficult to conceive of entropy. Origin and first definition due to CLAUSIUS; some formulas for it available from the start. Its statistical character early appreciated; lack of precise physical meaning; its dependence on probability; number of complexions a synonym for probability37(2) PLANCK'Sformula for the relation between entropy and the number of complexions40Certain features of entropy41SECTION EEquivalents of change of entropy in more or less general physical terms or aspects41Not surprising that its many forms should have been a reproach to the second law41General principles for comparing these aspects. Various aspects of growth of entropy from the experiential and from the atomic point of view42SECTION FMore precise and specific statements of the second law44General arrangement and the principles for comparison44Ten different statements of the law and comments thereon44PART IIANALYTICAL EXPRESSIONS FOR A FEW PRIMARY RELATIONSProcedure followed48SECTION AMaxwell's law of distribution of molecular velocities48Outline of proof, illustration, and consequences of this law48SECTION BSimple analytical expression for dependence of entropy on probability53PLANCK'S derivation; illustration, limitations, consequences, features and comments53SECTION CDetermination of a precise, numerical expression for the entropy of any physical configuration56BOLTZMANN'S pioneer work, PLANCK'S exposition, and the six main steps56Step aDetermination of the general expression for theof a given configuration of a known aggregate state57Step bDetermination of the general expression for the entropyof a given configuration of a known aggregate state63Step cSpecial case of (b), namely, expression for the entropyof the state of thermal equilibrium of a monatomic gas63Step dConfirmation, by equating this value ofwith that found thermodynamically and then deriving known results64Step ePLANCK'S conversion of the expressions of (b) and (c) into more precise ones by finding numerical value of66Step fDetermination of the dimensions of the universal constantand therefore also of entropy in general67PART IIITHE PHYSICAL INTERPRETATIONSSECTION AOf the simple reversible operations in thermodynamicsIsometric, isobaric, isothermal, and isentropic change69SECTION BOf the fundamentally irreversible processesHeat conduction, work into heat of friction, expansion without work, and diffusion of gases72SECTION COf negative change of entropySome of its physical features and necessary accompaniments78SECTION DPhysical significance of the equivalents for growth of entropy given on pp. 42-4380SECTION EPhysical significance of the more specific statements of second law given on pp. 44-4781PART IVSUMMARY OF THE CONNECTION BETWEEN PROBABILITY, IRREVERSIBILITY, ENTROPY, AND THE SECOND LAWSECTION A(1)Prerequisites and conditions necessary for the application of the theory of probabilities(a) Atomic theory; (b) like particles; (c) very numerous particles; (d) "elementary chaos"83(2)Differences in the states of "elementary chaos"85(3)Number of complexions, or probability of a chaotic state86SECTION BIrreversibility86SECTION CEntropy87SECTION DThe Second LawIts basis and best statements; it has noindependentsignificance88PART VREACH OR SCOPE OF THE SECOND LAWSECTION AIts extension to all bodiesPLANCK'S presentation; fifteen steps in the proof91SECTION BGeneral conclusion as to entropy changes98